In The Expanse, the future of humanity is constantly at stake. In The Expanse vestiges of an ancient alien civilization with incredibly advanced technology have been found—which eventually permits human interstellar expansion through the gates. James Lenman argues that, even if we agree that biodiversity is a good thing, it only means that it's good that there should be natural diversity while life exists on Earth. While we might not be facing interplanetary war or the unpredictable consequences of ancient (...) alien technology, many serious dangers face the human species today. We are quite resilient and have survived numerous disasters in the past, including floods, earthquakes, famine, pandemics, and wars. Small population size and restricted distribution range are factors that increase a species’ extinction risk. Interplanetary expansion could potentially bring about speciation, which means the separation of Homo sapiens into different species. (shrink)

Consider the expansion TS of a theory T by a predicate for a submodel of a reduct T0 of T. We present a setup in which this expansion admits a model companion TS. We show that some of the nice feat...

From the perspective of world philosophy, one phenomenon of the 20th century is quite intriguing. Certain philosophers in China as well as in the West, finding the traditional conception of epistemology too narrow-minded, argued that its scope should be expanded. The Chinese way of expanding epistemology might be called the metaphysical approach, and the Western way the practical approach. In this article, I will first give an outline of both approaches and then try to demonstrate that a substantial dialogue can (...) be created between them. By focusing on the problem of the articulation of what we know, I will make the metaphysical approach and the practical approach engage each other and thus prove to be mutually complementary. (shrink)

This paper proposes a new Separabilist account of thick concepts, called the Expansion View (or EV). According to EV, thick concepts are expanded contents of thin terms. An expanded content is, roughly, the semantic content of a predicate along with modifiers. Although EV is a form of Separabilism, it is distinct from the only kind of Separabilism discussed in the literature, and it has many features that Inseparabilists want from an account of thick concepts. EV can also give non-cognitivists (...) a novel escape from the Anti-Disentangling Argument. §I explains the approach of all previous Separabilists, and argues that there’s no reason for Separabilists to take this approach. §II explains EV. §III fends off objections. And §IV explains how non-cognitivist proponents of EV can escape the Anti-Disentangling Argument. (shrink)

Life expansion means increasing the length of time a person is alive and diversifying the matter in which a person exists. For human life, the length of time is bounded by a single century and its matter is tied to biology.

We investigate expansions of the ordered field of real numbers equipped with a family of real power functions. We show in particular that the theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization. We derive that every function of one variable definable in this structure, not ultimately identically 0, is asymptotic at + ∞ to a real function of the form x (...) cxr, c ≠ 0; in particular, this structure is polynomially bounded. Furthermore, given any definable function f:U → with U open in n, if α ε U and f is infinitely differentiable at α, then f is real analytic in a neighborhood of α. (shrink)

Induced by intake of the psychedelic substances LSD, psilocybin, DMT and mescaline, psychedelic experiences have been extensively described by subjects as entailing a most unusual increase in the scope and quality of their consciousness. Accordingly, psychedelic experiences have been widely characterised as an “expansion of consciousness.” This article poses the following question, as yet unaddressed in contemporary philosophy and the tradition of phenomenology: to what exactly does “expansion of consciousness” refer as a general characterisation of psychedelic experiences, and (...) what role might attention play therein? On the basis of Aron Gurwitsch’s phenomenology of attention, the following thesis is presented: (a) “expansion of consciousness” refers to a particular restructuration of consciousness in psychedelic experiences. (b) This occurs by means of certain extreme transformations in direction, scope, mode and degree of attention. In order to explicate this thesis, the characteristic features of psychedelic experiences that pertain to expansion of consciousness and attention are first systematically identified from a survey of subject reports. Second, it is demonstrated that the few previous attempts to understand expansion of consciousness in terms of attention as a filter/reducing-valve, spotlight or zoom-lens each fail to explain how consciousness is structured in psychedelic experiences. Third, it is argued that psychedelic expansion of consciousness is a general restructuration of consciousness by means of extreme attentional transformations. In conclusion, brief consideration is given to the question of whether psychedelic expansion of consciousness can have epistemic and ethical value for life. (shrink)

Let A be an abelian variety in an algebraically closed field of characteristic 0. We prove that the expansion of A by a generic divisible subgroup of A with the same torsion exists provided A has few algebraic endomorphisms, namely. The resulting theory is NSOP1 and not simple. Note that there exist abelian varieties A with of any genus.

Epistemology should take seriously the possibility of rationally evaluable changes in conceptual resources. Epistemic decision theory compares belief states in terms of epistemic value. But it's standardly restricted to belief states that don't differ in their conceptual resources. I argue that epistemic decision theory should be generalized to make belief states with differing concepts comparable. I characterize some possible constraints on epistemic utility functions. Traditionally, the epistemic utility of a total belief state has been understood as a function of the (...) epistemic utility of individual (partial) beliefs. The most natural ways of generalizing this account generate a kind of repugnant conclusion. I characterize some possible alternatives, reflecting different epistemic norms. (shrink)

Like philosophy itself, Dune explores everything from politics to art to life to reality, but above all, the novels ponder the mysteries of mind. Voyaging through psychic expanses, Frank Herbert hits upon some of the same insights discovered by indigenous people from the Americas. Many of these ideas are repeated in mainstream American and European philosophical traditions like pragmatism and existential phenomenology. These outlooks share a regard for mind as ecological, which is more or less to say that minds extend (...) beyond the brain into the rest of the body and the surrounding environment. -/- The cross-cultural strands in Dune tie closely to Herbert’s life and interests. An outdoorsman born in the Pacific West, he had an abiding bond with a friend from the Quileute tribe, Howie Hansen. Herbert advocated for aboriginal rights and crafted well-intentioned if slightly stereotypical tales about indigenous characters, partly based on his visits with Northwest tribes. Carl Jung (1875-1961), whose idea of collective consciousness echoes aboriginal views, was among Herbert’s European influences. So was existential phenomenology, especially as developed by Martin Heidegger (1889-1976). The names of characters in one of Herbert’s novels—The Santaroga Barrier—in fact coincide with terms that Heidegger used to articulate how emotionally colored coping with our environment defines our existence. Many indigenous philosophers have treated phenomenology and its American cousin pragmatism in approving ways. Indeed, the ideas of North America’s first inhabitants seem to have been absorbed by pragmatists and even earlier by transcendentalists like Ralph Waldo Emerson (1803-1882) and Henry David Thoreau (1817-1862). -/- These different philosophies all advance a place-based psychology. Anne Waters, herself of mixed tribal heritage, generalizes the mindset of her people this way: “American Indian consciousness, and hence American Indian identity is … interdependent with our land base.” Lee Hester, a Choctaw thinker, adds that practices—not mere beliefs—are most important for native thought. American transcendentalists and pragmatists, as well as European phenomenologists, similarly see hands-on practices and environmental interactions as the core of experience. Extending this a little, they sometimes suggest experience isn’t individual but instead cultural. “Culture” is here understood as interactions within communities that define our worlds and experiences, as when we talk about the “French experience,” “culture” or “world,” or the “experience of parenthood.” This theme also shows up in indigenous thought. -/- Exploring the Dune universe, we find everything from land-based concepts of personal identity, to the idea of sharpening the mind through hands-on training, to collective notions of experience in cooperative tribes or through the genetic memory of central characters. The stories explore fate versus free will in cosmic contexts, introducing views from indigenous thought and the pragmatic philosophy of William James (1842-1910). Different forms of spiritualism mingle to shape minds and cultural mixtures around the globe, and the same occurs in the Dune series. The customs and personalities of characters fuse elements from Buddhism, Christianity, Hinduism, Judaism, Taoism, and especially Islam. The series not only highlights that religion shapes psychology, but also that faith connects to place, especially paralleling Judeo-Christian-Islamic desert faiths. In capturing these points, the Dune novels show that “our values, our lifestyles and even the ways we think and feel have been strongly influenced by our locations in history and geography. The study of the human mind is fundamentally the study of place.”. (shrink)

We consider the question of when an expansion of a first-order topological structure has the property that every open set definable in the expansion is definable in the original structure. This question has been investigated by Dolich, Miller and Steinhorn in the setting of ordered structures as part of their work on the property of having o-minimal open core. We answer the question in a fairly general setting and provide conditions which in practice are often easy to check. (...) We give a further characterisation in the special case of an expansion by a generic predicate. (shrink)

An open U ⊆ ℝ is produced such that (ℝ, +, ·, U) defines a Borel isomorph of (ℝ, +, ·, ℕ) but does not define ℕ. It follows that (ℝ, +, ·, U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (ℝ, +, ·). In particular, there is a Cantor set E ⊆ ℝ (...) such that (ℝ, +, ·, E) defines a Borel isomorph of (ℝ, +, ·, ℕ) and, for every exponentially bounded o-minimal expansion $\germ{R}$ of (ℝ, +, ·), every subset of ℝ definable in ( $\germ{R}$ , E) either has interior or is Hausdorff null. (shrink)

The article discusses the expansion of the Islamic extremist groups in the Lake Chad basin countries. The geopolitical zones and states of Nigeria, regions of Niger and Cameroon, macro-regions of Chad were selected as the territorial range. The religious affiliation data has been compiled from the DHS-database. Income levels and literacy rates were evaluated indirectly using body mass index and the degree of age-heaping, respectively. A hierarchical cluster analysis, has allowed us to categorize the territorial-administrative units into four groups (...) by the probability of new Islamic extremist groups appearing there. The article clearly shows that Boko Haram may expand in the Western and North-Western directions. Meanwhile, the new cells are more likely to form inside Nigeria than outside it. Thus, in the near future, theexpansion of Islamic extremist organizations in the Lake Chad basin countries will occur at the local level. Keywords: Lake Chad basin countries, Islamic Extremism, Boko Haram, expansion. (shrink)

Analizaremos algunos rasgos del proceso de transformación económica y social que tuvo lugar en al-Andalus entre los siglos X y XII, en el marco de la «revolución económica» de la Europa plenomedieval, tomando como caso de estudio la región oriental de la península ibérica. El proceso debió de arrancar con un despegue demográfico y con el aumento de la productividad agrícola, en este caso derivado de los progresos técnicos asociados a la llamada «revolución verde» islámica de los siglos VIII al (...) X. El incremento creciente de los beneficios derivados del campo y el interés por aprovecharlos seguramente impulsó la coacción de las élites urbanas sobre las comunidades campesinas para arrebatarles las tierras más rentables. También pudo ocasionar la colonización de áreas rurales menos favorecidas, que hasta ese momento habían permanecido incultas, por parte de esos grupos acomodados que buscaban expandir los cultivos comerciales, así como por familias de campesinos desposeídos de las mejores tierras. Los cambios en el mundo rural influyeron en el crecimiento de las ciudades debido a la inmigración de la población del campo, presionada y desplazada, que se incorporaba como proletariado urbano ante el incremento en la demanda de manufacturas y bienes de consumo por parte de los terratenientes enriquecidos que habitaban esas ciudades. (shrink)

This paper is a contribution toward developing a theory of expansions of semi-Heyting algebras. It grew out of an attempt to settle a conjecture we had made in 1987. Firstly, we unify and extend strikingly similar results of [ 48 ] and [ 50 ] to the (new) equational class DHMSH of dually hemimorphic semi-Heyting algebras, or to its subvariety BDQDSH of blended dual quasi-De Morgan semi-Heyting algebras, thus settling the conjecture. Secondly, we give a criterion for a unary (...) class='Hi'>expansion of semi-Heyting algebras to be a discriminator variety and give an algorithm to produce discriminator varieties. We then apply the criterion to exhibit an increasing sequence of discriminator subvarieties of BDQDSH . We also use it to prove that the variety DQSSH of dually quasi-Stone semi- Heyting algebras is a discriminator variety. Thirdly, we investigate a binary expansion of semi-Heyting algebras, namely the variety DblSH of double semi-Heyting algebras by characterizing its simples, and use the characterization to present an increasing sequence of discriminator subvarieties of DblSH . Finally, we apply these results to give bases for “small” subvarieties of BDQDSH , DQSSH , and DblSH. (shrink)

Dune explores everything from politics to art to life to reality, but, the novels ponder the mysteries of mind. Dune explores everything from politics to art to life to reality, but above all, the novels ponder the mysteries of mind. Many of these ideas are repeated in mainstream American and European philosophical traditions like pragmatism and existential phenomenology. Exploring the Dune universe, can find everything from land based concepts of personal identity, to the idea of sharpening the mind through hands (...) on training, to collective notions of experience in cooperative tribes or through the genetic memory of central characters. The sandworms make both the spice and the desert they need to survive. Tribal existence has levels of direct cooperaion that make it hard not to celebrate and occasionally mourn the group aspects of life. (shrink)

An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists! \mathop{\boldsymbol {\bigwedge }}\limits p = q$. For a logic L algebraized by a quasivariety $\mathcal {Q}$ we show that the AE-subclasses of $\mathcal {Q}$ correspond to certain natural expansions of L, which we call algebraic expansions. These turn out to be a special case of the expansions by implicit connectives studied by X. Caicedo. We proceed to characterize all the AE-subclasses of (...) abelian $\ell $ -groups and perfect MV-algebras, thus fully describing the algebraic expansions of their associated logics. (shrink)

Let P be the ω-orbit of a point under a unary function definable in an o-minimal expansion ℜ of a densely ordered group. If P is monotonically cofinal in the group, and the compositional iterates of the function are cofinal at +\infty in the unary functions definable in ℜ, then the expansion (ℜ, P) has a number of good properties, in particular, every unary set definable in any elementarily equivalent structure is a disjoint union of open intervals and (...) finitely many discrete sets. (shrink)

Este artículo reflexiona sobre la segregación socio-espacial en contextos urbanos, comprendiéndola como una dimensión particular de los procesos de estructuración social en las ciudades capitalistas. Concretamente, se aborda el caso de la ciudad de Córdoba (Argentina). Se parte del supuesto de que el crecimiento urbano por expansión que se registra durante la década del `80, es el resultado de un doble proceso de larga duración. Por un lado, políticas de desarrollo urbano que buscan incrementar la productividad y atraer inversiones privadas (...) que re-cualifiquen espacios estratégicos de la ciudad. Por otro lado, y subsidiario del proceso anterior, la progresiva ocupación diferencial del área periférica de acuerdo a posiciones y condiciones de clase. Se concluye que la suburbanización que se registra en la ciudad forma parte de una política general de (re)valorización urbana orientada hacia el capital privado, y que ya desde los primeros años de la transición democrática pueden observarse en Córdoba incipientes marcas de una periferia segmentada en términos de clase. La estrategia metodológica articula el análisis de datos provenientes de fuentes secundarias (indicadores urbanos, socio-demográficos y habitacionales) con el abordaje cualitativo de intervenciones urbanas y marcos normativos sancionados a mediados de la década del ’80. (shrink)

For centuries, the processes of social differentiation associated with Modernity have often been thought to intensify the need for site-specific forms of role training and knowledge production, threatening the university’s survival either through fragmentation or through failure to adapt. Other lines of argument emphasize the extent to which the Modern system creates and relies on an integrated knowledge system, but most of the literature stresses functional differentiation and putative threats to the university. And yet over this period the university has (...) flourished. In our view, this seeming paradox is explained by the fact that modern society rests as much on universalistic cosmological bases as it does on differentiation. The university expands over recent centuries because – as it has from its religious origins – it casts cultural and human materials in universalistic terms. Our view helps explain empirical phenomena that confound standard accounts: the university’s extraordinary expansion and global diffusion, its curricular and structural isomorphism, and its relatively unified structure. All of this holds increasingly true after World War II, as national state societies made up of citizens are increasingly embedded in a world society constituted of empowered individuals. The redefinition of society in global and individual terms reduces nationally bounded models of nature and culture, extends the pool of university beneficiaries and investigators, and empowers the human persons who are understood to root it all. The changes intensify universalization and the university’s rate of worldwide growth. For the university’s knowledge and “knowers,” and for the pedagogy that joins them together, the implications are many. The emerging societal context intensifies longstanding processes of cultural rationalization and ontological elaboration, yielding great expansions in what can and should be known, and in who can and should know. These changes in turn alter the menu of approved techniques for joining knowledge and knower as one. The “knowledge society” that results is distinguished by the extraordinary degree to which the university is linked to society. But it is also distinguished by the degree to which society is organized around the university’s abstracted and universalized understandings of the world and its degree-certified graduates. (shrink)

The Expanse does not provide an easy answer to the vexing question on making a decision when competing, but considering conflicts of values on the show can help us reason about tough choices in real life. Sometimes, scientific progress conflicts with the prudential value of self‐preservation. This chapter explains three ways of understanding value conflicts: as situations in which every option is forbidden, situations in which every option is permissible, or situations in which some options are obligatory and some options (...) are forbidden. The idea that all these different kinds of value can be traded with a common currency is tempting. But contra Keats, beauty is not truth; and it certainly is not goodness, as Tolstoy says. Epistemic, moral, prudential, and aesthetic values are very different. (shrink)

Call a (strictly increasing) sequence (rn) of natural numbers regular if it satisfies the following condition: rn+1/rn→θ∈R>1∪{∞} and, if θ is algebraic, then (rn) satisfies a linear recurrence relation whose characteristic polynomial is the minimal polynomial of θ. Our main result states that (Z,+,0,R) is superstable whenever R is enumerated by a regular sequence. We give two proofs of this result. One relies on a result of E. Casanovas and M. Ziegler and the other on a quantifier elimination result. We (...) also show that (Z,+,0,<,R) is NIP whenever R is enumerated by a regular sequence that is ultimately periodic modulo m for all m>1. (shrink)

A subset A $\subseteq$ M of a totally ordered structure M is said to be convex, if for any a, b $\in A: [a . A complete theory of first order is weakly o-minimal (M. Dickmann [D]) if any model M is totally ordered by some $\emptyset$ -definable formula and any subset of M which is definable with parameters from M is a finite union of convex sets. We prove here that for any model M of a weakly o-minimal theory (...) T, any expansion M + of M by a family of unary predicates has a weakly o-minimal theory iff the set of all realizations of each predicate is a union of a finite number of convex sets (Theorem 63), that solves the Problem of Cherlin-Macpherson-Marker-Steinhorn [MMS] for the class of weakly o-minimal theories. (shrink)

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.

In The Expanse, the major powers do a great deal of talking, but don't have a great deal of understanding. Discussing language can be surprisingly difficult, because the only way to discuss language is with language and that peculiar arrangement can lead to some outright strangeness. Eccentric, reclusive, and hot‐tempered, Ludwig Wittgenstein is a key philosopher in the examination of language and meaning. Wittgenstein's philosophical studies centered around how to express meaning and why conveying meaning so often breaks down. In (...) Wittgenstein's earlier writings he articulates the picture book model of language. Language can be written, spoken, signed, and so forth, but it is convention to refer to any language user as a ‘speaker.’ Wittgenstein argues that language works much like a game, relying on contextual rules and actions to guide and form meaning. The language game model of language also better explains why Belters and the Inners seem doomed to fail to communicate. (shrink)

LetMbe a countably infinite ω-categorical structure. Consider Aut(M) as a complete metric space by definingd(g, h) = Ω{2−n:g(xn) ≠h(xn) org−1(xn) ≠h−1(xn)} where {xn:n∈ ω} is an enumeration ofMAn automorphism α ∈ Aut(M) is generic if its conjugacy class is comeagre. J. Truss has shown in [11] that if the set P of all finite partial isomorphisms contains a co-final subset P1closed under conjugacy and having the amalgamation property and the joint embedding property then there is a generic automorphism. In the (...) present paper we give a weaker condition of this kind which is equivalent to the existence of generic automorphisms. Really we give more: a characterization of the existence of generic expansions (defined in an appropriate way) of an ω-categorical structure. We also show that Truss' condition guarantees the existence of a countable structure consisting of automorphisms ofMwhich can be considered as an atomic model of some theory naturally associated toM. We do it in a general context of weak models for second-order quantifiers.The author thanks Ludomir Newelski for pointing out a mistake in the first version of Theorem 1.2 and for interesting discussions. Also, the author is grateful to the referee for very helpful remarks. (shrink)

Let ℜ be an o-minimal expansion of (ℝ, <+) and (φk)k∈ℕ be a sequence of positive real numbers such that limk→+∞f(φk)/φk+1=0 for every f:ℝ→ ℝ definable in ℜ. (Such sequences always exist under some reasonable extra assumptions on ℜ, in particular, if ℜ is exponentially bounded or if the language is countable.) Then (ℜ, (S)) is d-minimal, where S ranges over all subsets of cartesian powers of the range of φ.

A goal of expanding life over time, space, and substrate requires that we look beneath the surface of technology and the universal norms placed on human nature to a vision of its future that could be realized. There is a visible fracturing of the personal and social behaviors of its hybrid users – a process that we might call data‐clatter. While life expansion seeks the continuation of persons over time and space and beyond the physical body, there is no (...) current method for backing up the brain and transferring its processes outside the biological system. The objectives of life expansion include developing a whole‐body prosthesis as both a device for mobility and sensory perception and a system that streams cognitive functions. These systems would provide the biosphere for biological systems of humans and the cybersphere for computational systems of digital persons. (shrink)

We develop a probabilistic criterion for belief expansion that is sensitive to the degree of contextual fit of the new information to our belief set as well as to the reliability of our information source. We contrast our approach with the success postulate in AGM-style belief revision and show how the idealizations in our approach can be relaxed by invoking Bayesian-Network models.

Capitalism’s Expansion into the Realm of the Biosphere. The extension of the rule of industrial property over living organisms and their components – genes and cells, both human and non-human – since the end of the 1970s, has gone along with the emergence of new markets in science, biotechnology and in health. The article argues that the filing of patents to protect private claims on living matter is a development which promotes the establishment of a monopoly control over inventions (...) in the fields of medicine and agronomy, while at the same time fostering a restriction in exchanges within the scientific community. The article therefore argues the case for a declaration that genomes, human and non-human, be considered as a common good, in terms both of the research carried out for the improvement of plants and health and of the accessibility of the medical innovations resulting from such research. (shrink)

We develop a probabilistic criterion for belief expansion that is sensitive to the degree of contextual fit of the new information to our belief set as well as to the reliability of our information source. We contrast our approach with the success postulate in AGM-style belief revision and show how the idealizations in our approach can be relaxed by invoking Bayesian-Network models.

A fascinating recent turn in epistemology focuses on inquiring attitudes like wondering and being curious. Many have argued that these attitudes are governed by norms similar to those that govern our doxastic attitudes. Yet, to date, this work has only considered norms that might *prohibit* having certain inquiring attitudes (``norms of restriction''), while ignoring those that might *require* having them (``norms of expansion''). We aim to address that omission by offering a framework that generates norms of expansion for (...) inquiring attitudes. The framework draws on inferential erotetic logic, which we explain and augment with some theorems. We explore several of the norms that it yields - some sympathetically, others unsympathetically. (shrink)

The ability to be creative is often considered a unique characteristic of conscious beings and many efforts have been directed at demonstrating a relationship between creativity and the personality construct of psychoticism. The present study sought to investigate this link explicitly by focusing on discrete facets of creative cognition, namely the originality/novelty dimension and the practicality/usefulness dimension. Based on Eysenck’s conceptualisation of psychoticism as being characterised by an overinclusive cognitive style, it was expected that higher levels of psychoticism would accompany (...) a greater degree of conceptual expansion and elevated levels of originality in creative imagery, but would be unrelated to the practicality/usefulness of an idea. These hypotheses were confirmed in 80 healthy participants who were contrasted based on their EPQ psychoticism scale scores. Our findings suggest that the link between psychoticism and creativity is based on associative thinking and broader but weak top-down activation patterns rather than on goal-related thinking. (shrink)

We study groups definable in tame expansions of ω-stable theories. Assuming several tameness conditions, we obtain structural theorems for groups definable and interpretable in these expansions. As our main example, by characterizing independence in the pair, where K is an algebraically closed field and G is a multiplicative subgroup of K× with the Mann property, we show that the pair satisfies the assumptions. In particular, this provides a characterization of definable and interpretable groups in in terms of algebraic groups in (...) K and interpretable groups in G. Furthermore, we compute the Morley rank and the U-rank in and both ranks agree. (shrink)

Asian Expansions: The Historical Experiences of Polity Expansion in Asia. Edited by GEoff Wade. Routledge Studies in the Early History of Asia, vol. 9. Abingdon: Routledge, 2015. Pp. xii + 259. $145.

This thesis is concerned with the expansions of algebraic structures and their fit in Shelah’s classification landscape.The first part deals with the expansion of a theory by a random predicate for a substructure model of a reduct of the theory. Let T be a theory in a language $\mathcal {L}$. Let $T_0$ be a reduct of T. Let $\mathcal {L}_S = \mathcal {L}\cup \{S\}$, for S a new unary predicate symbol, and $T_S$ be the $\mathcal {L}_S$ -theory that axiomatises (...) the following structures: $$ consist of a model $\mathscr {M}$ of T and S is a predicate for a model $\mathscr {M}_0$ of $T_0$ which is a substructure of $\mathscr {M}$. We present a setting for the existence of a model-companion $TS$ of $T_S$. As a consequence, we obtain the existence of the model-companion of the following theories, for $p>0$ a prime number: • $\mathrm {ACF}_p$, $\mathrm {SCF}_{e,p}$, $\mathrm {Psf}_p$, $\mathrm {ACFA}_p$, $\mathrm {ACVF}_{p,p}$ in appropriate languages expanded by arbitrarily many predicates for additive subgroups;• $\mathrm {ACF}_p$, $\mathrm {ACF}_0$ in the language of rings expanded by a single predicate for a multiplicative subgroup;• $\mathrm {PAC}_p$ -fields, in an appropriate language expanded by arbitrarily many predicates for additive subgroups.From an independence relation in T, we define independence relations in $TS$ and identify which properties of are transferred to those new independence relations in $TS$, and under which conditions. This allows us to exhibit hypotheses under which the expansion from T to $TS$ preserves $\mathrm {NSOP}_{1}$, simplicity, or stability. In particular, under some technical hypothesis on T, we may draw the following picture : Configuration $T_0\subseteq T$ Generic expansion $TS$ $T_0 = T$ Preserves stability $T_0\subseteq T$ Preserves $\mathrm {NSOP}_{1}$ $T_0 = \emptyset $ Preserves simplicityIn particular, this construction produces new examples of $\mathrm {NSOP}_{1}$ not simple theories, and we study in depth a particular example: the expansion of an algebraically closed field of positive characteristic by a generic additive subgroup. We give a full description of imaginaries, forking, and Kim-forking in this example.The second part studies expansions of the group of integers by p-adic valuations. We prove quantifier elimination in a natural language and compute the dp-rank of these expansions: it equals the number of independent p-adic valuations considered. Thus, the expansion of the integers by one p-adic valuation is a new dp-minimal expansion of the group of integers. Finally, we prove that the latter expansion does not admit intermediate structures: any definable set in the expansion is either definable in the group structure or is able to “reconstruct” the valuation using only the group operation.prepared by Christian d’Elbée.E-mail: [email protected]: https://choum.net/~chris/page_perso. (shrink)

Accelerating Expansion explores some of the philosophical implications of modern cosmology, focused on the significance that the discovery of the accelerating expansion of the Universe has for our understanding of time, geometry, and physics. The appearance of the cosmological constant in the equations of general relativity allows one to model universes in which space has an inherent tendency towards expansion. This constant, introduced by Einstein but subsequently abandoned by him, returned to centre stage with the discovery of (...) the accelerating expansion. This pedagogically-oriented essay begins with a study of the most basic and elegant relativistic world that involves a positive cosmological constant, de Sitter spacetime. It then turns to the relatives of de Sitter spacetime that dominate modern relativistic cosmology. Some of the topics considered include: the nature of time and simultaneity in de Sitter worlds; the sense in which de Sitter spacetime is a powerful dynamical attractor; the limited extent to which observation can give us information about the topology of space in a world undergoing accelerated expansion; and cosmologists' favourite sceptical worry about the reliability of evidence and the possibility of knowledge, the problem of Boltzmann brains. (shrink)

We investigate expansions of Heyting algebras in possession of a unary term describing the filters that correspond to congruences. Hasimoto proved that Heyting algebras equipped with finitely many normal operators have such a term, generalising a standard construction on finite-type boolean algebras with operators. We utilise Hasimoto’s technique, extending the existence condition to a larger class of EHAs and some classes of double-Heyting algebras. Such a term allows us to characterise varieties with equationally definable principal congruences using a single equation. (...) Moreover, in the presence of a dual pseudocomplement operation, discriminator varieties are characterised by a pair of equations. We also prove that a variety of dually pseudocomplemented EHAs with a normal filter term is semisimple if and only if it is a discriminator variety. This generalises two known results, one by Kowalski and Kracht for finite-type varieties of BAOs, and the other by the present author for dually pseudocomplemented Heyting algebras without additional operations. (shrink)

We investigate expansions of Heyting algebras in possession of a unary term describing the filters that correspond to congruences. Hasimoto proved that Heyting algebras equipped with finitely many normal operators have such a term, generalising a standard construction on finite-type boolean algebras with operators. We utilise Hasimoto’s technique, extending the existence condition to a larger class of EHAs and some classes of double-Heyting algebras. Such a term allows us to characterise varieties with equationally definable principal congruences using a single equation. (...) Moreover, in the presence of a dual pseudocomplement operation, discriminator varieties are characterised by a pair of equations. We also prove that a variety of dually pseudocomplemented EHAs with a normal filter term is semisimple if and only if it is a discriminator variety. This generalises two known results, one by Kowalski and Kracht for finite-type varieties of BAOs, and the other by the present author for dually pseudocomplemented Heyting algebras without additional operations. (shrink)

Let ℛ be an o-minimal expansion of a real closed field R. We continue here the investigation we began in [11] of differentiability with respect to the algebraically closed field [Formula: see text]. We develop the basic theory of such K-differentiability for definable functions of several variables, proving theorems on removable singularities as well as analogues of the Weierstrass preparation and division theorems for definable functions. We consider also definably meromorphic functions and prove that every definable function which is (...) meromorphic on Kn is necessarily a rational function. We finally discuss definable analogues of complex analytic manifolds, with possible connections to the model theoretic work on compact complex manifolds, and present two examples of "nonstandard manifolds" in our setting. (shrink)

The generation of complex organ structures such as the eye requires the intricate orchestration of multiple cellular interactions. In this paper, early retinal development is discussed with respect to the structure formation of the optic cup. Although recent studies have elucidated molecular mechanisms of retinal differentiation, little is known about how the unique shape of the optic cup is determined. A recent report has demonstrated that optic‐cup morphogenesis spontaneously occurs in three‐dimensional stem‐cell culture without external forces, indicating a latent intrinsic (...) order to generate the structure. Based on this self‐organizing phenomenon, we introduce the “relaxation‐expansion” model to mechanically interpret the tissue dynamics that enable the spontaneous invagination of the neural retina. This model involves three consecutive local rules (relaxation, apical constriction, and expansion), and its computer simulation recapitulates the optic‐cup morphogenesis in silico. (shrink)