Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture (...) for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L. (shrink)
We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals. We discuss the general open question of elimination of imaginaries in an o-minimal structure.
Let $\mathcal{M}$ be an o-minimal expansion of a real closed field $R$. We define the notion of a lattice in a locally definable group and then prove that every connected, definably generated subgroup of $\langle R^{n},+\rangle$ contains a definable generic set and therefore admits a lattice.
We prove the Compact Domination Conjecture for groups definable in linear o-minimal structures. Namely, we show that every definably compact group G definable in a saturated linear o-minimal expansion of an ordered group is compactly dominated by (G/G 00, m, π), where m is the Haar measure on G/G 00 and π : G → G/G 00 is the canonical group homomorphism.
In this short note we provide an example of a semi-linear group G which does not admit a semi-linear affine embedding; in other words, there is no semi-linear isomorphism between topological groups f:G→G′Mm, such that the group topology on G′ coincides with the subspace topology induced by Mm.
Let $\scr{M}=\langle M,+,<,0,S\rangle $ be a linear o-minimal expansion of an ordered group, and $G=\langle G,\oplus ,e_{G}\rangle $ an n-dimensional group definable in $\scr{M}$ . We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex ${\ssf V}\text{-definable}$ subgroup U of $\langle M^{n},+\rangle $ and a lattice L of rank equal to the dimension of the 'compact part' of G.
In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical (...) extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in [FIT 92a]. The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. (shrink)
Suppose G is a definably connected, definable group in an o-minimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism equation image: equation image→ G is a locally definable covering homomorphism and π1 is isomorphic to the o-minimal fundamental group π of G defined using locally definable covering homomorphisms.
In this note we show: Let R = 〈R, <, +, 0, …〉 be a semi-bounded o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m . Then G is a definable extension of a bounded definable group B by 〈Rm, +〉.
Let \ be an expansion of a real closed field \ by a dense subgroup G of \ with the Mann property. We prove that the induced structure on G by \ eliminates imaginaries. As a consequence, every small set X definable in \ can be definably embedded into some \, uniformly in parameters. These results are proved in a more general setting, where \ is an expansion of an o-minimal structure \ by a dense set \, satisfying three tameness (...) conditions. (shrink)
We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invariant of the group at hand. The analysis first goes through a local level, where a pertinent notion of pregeometry and (...) generic elements is each time introduced. (shrink)
We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. 18 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds (...) when [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text]. (shrink)
Introducing a largely neglected area of existing interactions between Greco-Roman antiquity and media theory, this volume brings together a range of interdisciplinary studies to address the question of why interactions in this area matter and how they might be developed further.
This is the second edition of Aristotle’s Metaphysics Lambda within two years, following Silvia Fazzo’s Il libro Lambda della Metafisica di Aristotele. Unlike Fazzo, Alexandru does not accompany the Greek text with a translation, but he should be thanked for providing a most valuable and exhaustive critical apparatus, which makes almost unnecessary any further work on the available sources. Alexandru has examined with great accuracy all forty-three Greek manuscripts that transmit Lambda and has fully collated the thirteen manuscripts that are (...) independent according to the stemma codicum established by Dieter Harlfinger; he adds to them a hitherto unknown manuscript of the β-family, namely the... (shrink)
In this paper I wish to discuss some relationships between philosophy and science, or rather, between the philosophy of science and the natural sciences, as well as the role of research programmes in these relationships. My interest in the topic rises out of the problems involved in teaching philosophy, and especially epistemology, to science, engineering and technology students. My “field experience” in the last five years has led me to the conclusion that the purpose is better served through a programme (...) of courses of different levels carried out by the joined forces and complementary efforts of philosophers and scientists. However, I do not intend to discuss either this conclusion or my own teaching experiences concerning a particular educational system at a particular period — in fact, one of reformation. If I mention this, it is in order to draw attention to two implicit distinctions, made by teachers and students, philosophers and scientists, but not always in the same manner, which may become the source of dispute when one attempts to make them explicit. The two distinctions are (a) the one between philosophy (of science) and (the natural) science(s), and (b) the one between the view of science presented in the philosophy of science and the view of science created by the scientists and science teachers. (shrink)
The influential threat simulation theory asserts that dreaming yields adaptive advantage by providing a virtual environment in which threat-avoidance may be safely rehearsed. We have previously found the incidence of biologically threatening dreams to be around 20%, with successful threat avoidance occurring in approximately one-fifth of such dreams. TST asserts that threat avoidance is over-represented relative to other possible dream contents. To begin assessing this issue, we contrasted the incidence of ‘avoidance’ dreams with that of their opposite: ‘approach’ dreams. Because (...) TST states that the threat-avoidance function is only fully activated in ecologically valid contexts, we also performed this contrast for populations living in both high- and low-threat environments. We find that ‘approach’ dreams are significantly more prevalent across both contexts. We suggest these results are more consistent with the view that dreaming is generated by reward-seeking systems than by fear-conditioning systems, although reward-seeking is clearly not the only factor determining the content of dreams. (shrink)
