We study the class of ω-categorical structures with n-degenerate algebraic closure for some n ε ω, which includes ω-categorical structures with distributive lattice of algebraically closed subsets , and in particular those with degenerate algebraic closure. We focus on the models of ω-categorical universal theories, absolutely ubiquitous structures, and ω-categorical structures generated by an indiscernible set. The assumption of n-degeneracy implies total categoricity for the first class, stability for the second, and ω-stability for the third.

The weak non-finite cover property (wnfcp) was introduced in [1] in connection with "axiomatizability" of lovely pairs of models of a simple theory. We find a combinatorial condition on a simple theory equivalent to the wnfcp, yielding a direct proof that the non-finite cover property implies the wnfcp, and that the wnfcp is preserved under reducts. We also study the question whether the wnfcp is preserved when passing from a simple theory T to the theory TP of lovely pairs of (...) models of T (true in the stable case). While the question remains open, we show, among other things, that if (for a T with the wnfcp) TP is low, then TP has the wnfcp. To study this question, we describe "double lovely pairs", and, along the way, we develop the notion of a "lovely n-tuple" of models of a simple theory, which is an analogue of the notion of a beautiful tuple of models of stable theories [2]. (shrink)

For a supersimple SU-rank 1 theory T we introduce the notion of a generic elementary pair of models of T . We show that the theory T* of all generic T-pairs is complete and supersimple. In the strongly minimal case, T* coincides with the theory of infinite dimensional pairs, which was used in 1184–1194) to study the geometric properties of T. In our SU-rank 1 setting, we use T* for the same purpose. In particular, we obtain a characterization of linearity (...) for SU-rank 1 structures by giving several equivalent conditions on T*, find a “weak” version of local modularity which is equivalent to linearity, show that linearity coincides with 1-basedness, and use the generic pairs to “recover” projective geometries over division rings from non-trivial linear SU-rank 1 structures. (shrink)

We continue the study of the connection between the “geometric” properties of SU -rank 1 structures and the properties of “generic” pairs of such structures, started in [8]. In particular, we show that the SU-rank of the theory of generic pairs of models of an SU -rank 1 theory T can only take values 1 , 2 or ω, generalizing the corresponding results for a strongly minimal T in [3]. We also use pairs to derive the implication from pseudolinearity to (...) linearity for ω -categorical SU -rank 1 structures, established in [7], from the conjecture that an ω -categorical supersimple theory has finite SU -rank, and find a condition on generic pairs, equivalent to pseudolinearity in the general case. (shrink)

We study expansions of an algebraically closed field K or a real closed field R with a linearly independent subgroup G of the multiplicative group of the field or the unit circle group \\), satisfying a density/codensity condition. Since the set G is neither algebraically closed nor algebraically independent, the expansion can be viewed as “intermediate” between the two other types of dense/codense expansions of geometric theories: lovely pairs and H-structures. We show that in both the algebraically closed field and (...) real closed field cases, the resulting theory is near model complete and the expansion preserves many nice model theoretic conditions related to the complexity of definable sets such as stability and NIP. (shrink)

Given a lovely pair P ≺ M of models of a simple theory T, we study the structure whose universe is P and whose relations are the traces on P of definable (in ℒ with parameters from M) sets in M. We give a necessary and sufficient condition on T (which we call weak lowness) for this structure to have quantifier-elimination. We give an example of a non-weakly-low simple theory.

We study the theory of the structure induced by parameter free formulas on a “dense” algebraically independent subset of a model of a geometric theory T. We show that while being a trivial geometric theory, inherits most of the model theoretic complexity of T related to stability, simplicity, rosiness, the NIP and the NTP2. In particular, we show that T is strongly minimal, supersimple of SU‐rank 1, has the NIP or the NTP2 exactly when has these properties. We show that (...) if T is superrosy of thorn rank 1, then so is, and that the converse holds if T satisfies acl = dcl. (shrink)

We study the theory of lovely pairs of geometric structures, in particular o-minimal structures. We use the pairs to isolate a class of geometric structures called weakly locally modular which generalizes the class of linear structures in the settings of SU-rank one theories and o-minimal theories. For o-minimal theories, we use the Peterzil–Starchenko trichotomy theorem to characterize for a sufficiently general point, the local geometry around it in terms of the thorn U-rank of its type inside a lovely pair.

We study definable groups in dense/codense expansions of geometric theories with a new predicate P such as lovely pairs and expansions of fields by groups with the Mann property. We show that in such expansions, large definable subgroups of groups definable in the original language \ are also \-definable, and definably amenable \-definable groups remain amenable in the expansion. We also show that if the underlying geometric theory is NIP, and G is a group definable in a model of T, (...) then the connected component \ of G in the expansion agrees with the connected component \ in the original language. We prove similar preservation results for \^n\), the P-part of G in a lovely pair, and for subgroups of G in pairs where R is a real closed field and G is a subgroup of \ or the unit circle \\) with the Mann property. (shrink)

We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new conditions equivalent to weak local modularity: "weak one-basedness", absence of type definable "almost quasidesigns", and "generic linearity". Among other things, we show that weak one-basedness is closed under reducts. We also show that the lovely pair expansion of a non-trivial weakly one-based ω-categorical geometric theory interprets an infinite vector space over (...) a finite field. (shrink)

We introduce the notion of a lovely pair of models of a simple theory T, generalizing Poizat's “belles paires” of models of a stable theory and the third author's “generic pairs” of models of an SU-rank 1 theory. We characterize when a saturated model of the theory TP of lovely pairs is a lovely pair , finding an analog of the nonfinite cover property for simple theories. We show that, under these hypotheses, TP is also simple, and we study forking (...) and canonical bases in TP. We also prove that assuming only that T is low, the existentially universal models of the universal part of a natural expansion TP+ of TP, are lovely pairs, and “simple Robinson universal domains”. (shrink)

Based on the work done in [][] in the o‐minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking‐independent elements that is dense inside a partial type, which we call H‐structures. We show that any two such expansions have the same theory and that under some technical conditions, the saturated models of this common theory are again H‐structures. We prove that under these assumptions the expansion is supersimple and (...) characterize forking and canonical bases of types in the expansion. We also analyze the effect these expansions have on one‐basedness and CM‐triviality. In the one‐based case, when T has SU‐rank and the SU‐rank is continuous, we take to be the type of elements of SU‐rank and we describe a natural “geometry of generics modulo H” associated with such expansions and show it is modular. (shrink)

In applied problems mathematics is used as language or as a metalanguage on which metatheories are built, E.G., Mathematical theory of experiment. The structure of pure mathematics is grammar of the language. As opposed to pure mathematics, In applied problems we must keep in mind what underlies the sign system. Optimality criteria-Axioms of applied mathematics-Prove mutually incompatible, They form a mosaic and not mathematical structures which, According to bourbaki, Make mathematics a unified science. One of the peculiarities of applied mathematical (...) language is a variety of dialects: a problem can be presented in terms of various mathematical notions. Another peculiarity is polysemy: a problem can be presented in the framework of one dialect by a set of various models with equal right to exist. The pragmatic sense of distinction between applied and pure mathematics must lead to specific training in each case. (shrink)

Lead shot deposited in fields and woodlands near shooting rangesand intense, upland, hunting adds an enormous tonnage of lead toenvironments, worldwide. This contamination is not remedied bybanning lead shot use only for waterfowl hunting. Lead pelletsdisintegrate extremely slowly, during which time they may beingested from the soil by wild birds, livestock, or silage-makingmachinery, and cause sublethal or fatal lead poisoning. Leadpellet corrosion products contaminate soil, surface waters, andground waters, often exceeding permissible levels. Plants do notconcentrate much lead from the soil, (...) except when grown in acidicsoils of heavily-contaminated shooting ranges. Inheavily-contaminated sites, earthworms ingest leadcompounds which are bioaccumulated in higher consumersof food webs. Non-toxic substitutes made from steelor bismuth are available internationally and areeffective for all types of hunting and targetshooting. Many nations are slow to require their use,despite the marked awareness of the problems of leadshot contamination and toxicosis. This is due tohunters and international sport shooting organizationsopposing the use of non-toxic substitutes and overtemphasis by government agencies on the burden ofscientific proof for every situation, rather thantaking preventative action according to thePrecautionary Principle. The ethical approach ofDenmark and The Netherlands, which banned all uses oflead shot, is advocated as a precedent for othernations to adopt. (shrink)

Moral philosophers have often felt the need of a concept which would cover all those cases where we are prevented from achieving our ends through no fault of our own: a criterion for saying when failure is not blameworthy. The deontologists thought we were not to blame for actions done in genuine ignorance of the facts. Kant declared in a famous passage that we were not morally responsible for failures due to the “niggardliness of stepmother nature.” In this article I (...) want to introduce into moral philosophy a new concept for clarifying the failures for which we are not to blame: the notion of scarcity, taken from economic theory. (shrink)

In this paper we present an executable approach to model interactions between agents that involve sensitive, privacy-related information. The approach is formal and based on deontic, epistemic and action logic. It is conceptually related to the Belief-Desire-Intention model of Bratman. Our approach uses the concept of sphere as developed by Waltzer to capture the notion that information is provided mostly with restrictions regarding its application. We use software agent technology to create an executable approach. Our agents hold beliefs about the (...) world, have goals and commitment to the goals. They have the capacity to reason about different courses of action, and communicate with one another. The main new ingredient of our approach is the idea to model information itself as an intentional agent whose main goal it is to preserve the integrity of the information and regulate its dissemination. We demonstrate our approach by applying it to an important process in the insurance industry: applying for a life insurance. In this paper we will: (1) describe the challenge organizational complexity poses in moral reasoning about informational relationships; (2) propose an executable approach, using software agents with reasoning capacities grounded in modal logic, in which moral constraints on informational relatio nships can be modeled and investigated; (3) describe the details of our approach, in which information itself is modeled as an intentional agent in its own right; (4) test and validate it by applying it to a concrete ‘hard case’ from the insurance industry; and (5) conclude that our approach upholds and offers potential for both research and practical application. (shrink)

Although research into the biosemiotic mechanisms underlying the purposeful behavior of brainless living systems is extensive, researchers have not adequately described biosemiosis among neurons. As the conscious use of signs is well-covered by the various fields of semiotics, we focus on subconscious sign action. Subconscious semiotic habits, both functional and dysfunctional, may be created and reinforced in the brain not necessarily in a logical manner and not necessarily through repeated reinforcement. We review literature that suggests hypnosis may be effective in (...) changing subconscious dysfunctional habits, and we offer a biosemiotic framework for understanding these results. If it has been difficult to evaluate any psychological approach, including hypnosis, this may be because contemporary neuroscience lacks a theory of the sign. We argue that understanding the fluid nature of representation in biological organisms is prerequisite to understanding the nature of the subconscious and may lead to more effective of treatments for dysfunctional habits developed through personal experience or culture. (shrink)

According to the traditional account Mendel's paper on pea hybrids reported a study of inheritance and its laws. Hence, Mendel came to be known as The Father of Genetics. This paper demonstrates that, in fact, Mendel's objective in his research was finding the empirical laws which describe the formation of hybrids and the development of their offspring over several generations. Having found these laws (and not the laws of inheritance that he is generally credited with) he proposed a theoretical scheme (...) involving the formation of germinal and pollen cells in hybrids and their combination in fertilization competent to explain why his laws took the form that they did. Mendel's research shows a pattern of development closely paralleling the stages of empirical investigation beginning at the level of qualitative description in common language rising through four levels of increasing abstraction and culminating in a fifth level, his simple mechanical theory. This mechanism met all the tests that a theory of this type must pass. In that respect Mendel was highly successful and this success might be the reason why he did not push his theory to a higher level, a sixth level involving the use of particulate determiners; despite this fact, Mendel was credited with having taken exactly that step. (shrink)

In this book, the extend to which we can equip artificial agents with moral reasoning capacity is investigated. Attempting to create artificial agents with moral reasoning capabilities challenges our understanding of morality and moral reasoning to its utmost. It also helps philosophers dealing with the inherent complexity of modern organizations. Modern society with large multi-national organizations and extensive information infrastructures provides a backdrop for moral theories that is hard to encompass through mere theorising. Computerized support for theorising is needed to (...) be able to fully grasp and address the inherent complexity. Using moral reasoning capacity will help us addressing the challenges that technological artefacts pose. They do not only contain information about us, they start to act on our behalves.With the increasing autonomy comes an increased need to ensure that their behaviour is in line with what we expect from them. To investigate and address these issues a laboratoy for philosophy is outlined: SophoLab. It consists of a methodology; a framework of modal logic, DEAL; and multi-agent software systems. SophoLab provides the basis for an experimental, computational philosophy. Its viability and usefulness are demonstrated through several experiments. (shrink)

In an article which appeared a few years ago, entitled ‘God's Death’ , A.D. Smith launched one of the most interesting of recent attacks on the traditional doctrine of the Incarnation. Focusing on the death of Christ, he claimed to demonstrate the logical impossibility of Jesus having been both human and divine. Each of the premises of his argument was said to be a commitment of orthodox theology. He thus presented his reasoning as displaying an internal incoherence in that way (...) of thinking about divinity, humanity, and the person of Christ. The argument was basically quite simple: According to Christian theology and in concurrence with general thought on the matter, we must hold that human death involves the possibility of annihilation. As a man, Jesus of Nazareth faced and underwent a human death. He thus faced the possibility of annihilation. But orthodox theologians hold God to be of such an ontological status that no divine being could even possibly be annihilated. So no divine person could die a human death. From this follows the impossibility of the traditional claim that the Second Person of the divine Trinity became a man, lived a human life, and died a human death for us and our salvation. The qualitative difference between God and man is such as to render incarnational christology an incoherent theological stance. (shrink)

After learning about the concept of determinism, a natural tendency is to conclude that if anyone actually believed in the determinism of human nature, then all future human actions are "set out for us" or "cut and dried" and, in some sense, utterly unavoidable. Another way of referring to such inevitability is that human action appears to be..

The construct of “choking under pressure” is concerned with the phenomenon of unexpected, sudden, and significant declines in individual athletes’ performances in important situations and has received empirical attention in the field of sport psychology. Although a number of theories about the reasons for the occurrence of choking under pressure exist and several intervention approaches have been developed, underlying mechanisms of choking are still under debate and the effectiveness of existing interventions remains contested. These sudden performance declines also occur in (...) team sport. “Collective sport team collapse,” which describes the situation when an entire sport team underperforms significantly within an important competitive situation, has received less empirical attention, in comparison to individual choking research. While there are a few studies that have investigated causes of collective team collapse, understandably, there has been limited empirical investigation of preventative and intervention strategies. Although the two constructs appear to share several similar characteristics and mechanisms, research has not yet examined the conceptual, theoretical, empirical, and practical links between choking under pressure and collective sport team collapse. In this review article, we seek to examine these similarities and differences and identify new ways of thinking about future interventions. Furthermore, current empirical understandings in the field of choking under pressure and collective sport team collapse are presented and the most effective intervention approaches for both constructs are introduced. On the basis of this examination, we modestly make some initial recommendations for sport psychological practitioners and future research. (shrink)

Of course you know the movie, just by cultural assimilation if not by having seen it. There’s this young elephant, Dumbo, who has laughably big ears and has been pitiably separated from his mom. He’s aided by a friendly talking mouse[ii] into translating those otherwise hapless ears into the power of flight, which he eventually uses to rescue his mom and live happily ever after. The way the wily mouse gets Dumbo to believe that he could fly is to give (...) him a “magic feather” which, held in his trunk, demonstrably imparts the gift of flight. Naturally the mouse believes throughout all this that Dumbo can fly anyway, but he also knows that Dumbo needs the feather as a confidence-builder to do so. At the critical juncture of the tale Dumbo loses the feather after being pushed off a precipice, and he thus plummets perilously towards earth—only to find at the last moment that he can indeed fly on his own. (shrink)

All right, first off I need to disappoint some people who despise reading the fine print on things or just plain love to speed-read only large fonts: this is not only not my last lecture, I m not even retiring anytime soon. So sorry to those of you poised to shout Good riddance to bad rubbish! at the end of this soliloquy. You re going to have to be patient a while longer.

Of course you know the movie, just by cultural assimilation if not by having seen it. There’s this young elephant, Dumbo, who has laughably big ears and has been pitiably separated from his mom. He’s aided by a friendly talking mouse2 into translating those otherwise hapless ears into the power of flight, which he eventually uses to rescue his mom and live happily ever after. The way the wily mouse gets Dumbo to believe that he could fly is to give (...) him a “magic feather” which, held in his trunk, demonstrably imparts the gift of flight. Naturally the mouse believes throughout all this that Dumbo can fly anyway, but he also knows that Dumbo needs the feather as a confidence-builder to do so. At the critical juncture of the tale Dumbo loses the feather after being pushed off a precipice, and he thus plummets perilously towards earth—only to find at the last moment that he can indeed fly on his own. (shrink)

Analysis shows that statements of ability are disguised conditionals. More exactly, the correct analysis of 'X could have done A' is 'If X h decided (chosen, willed ...) to do A, X would have done A'. Therefore having acted freely--having been able to act otherwise than one fact did--is compatible with determinism (with the causal determination of one's acts).