Related papers: On definable Skolem functions and trichotomy
We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…
We observe that the notion of a trivial Serre fibration, a Serre fibration, and being contractible, for finite CW complexes, can be defined in terms of the Quillen lifting property with respect to a single map M-->/\ of finite topological…
Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs…
The main result of this paper is a probabilistic construction of finite rigid structures. It yields a finitely axiomatizable class of finite rigid structures where no L^omega_{infty, omega} formula with counting quantifiers defines a linear…
We study definably amenable groups in NIP theories, and answer a question of Newelski (and also of Chernikov-Simon), by giving an example in the o-minimal context where weak generic types do not coincide with almost periodic types,…
A decidable transfinite hierarchy is defined by assigning ordinals to the programs of an imperative language. It singles out: the classes TIMEF(n^c) and TIMEF(n_c); the finite Grzegorczyk classes at and above the elementary level, and the…
It is well known that the R, the set of real numbers, is an abstract set, where almost all its elements cannot be described in any finite language. We investigate possible approaches to what might be called an epi-constructionist approach…
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…
The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on $^*$-algebras. We describe the extreme points of order intervals, and give a nontrivial sufficient…
Let m>2 be an integer. We show that ZF + "For every integer n, Every countable family of non-empty sets of cardinality at most n has an infinite partial choice function" is not strong enough to prove that every countable set of m-element…
Let $T$ be a theory which is t-minimal, meaning that with respect to some definable topology, a unary definable set $D \subseteq M$ has non-empty interior iff it is infinite. If $K$ is a definable field in $T$, then $K$ is finite or "large"…
This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…
We show that the derived subgroup of a linear definable group in an o-minimal structure is also definable, extending the semialgebraic case proved by A. Pillay. We also show the definability of the derived subgroup in case that the group is…
Finite topological spaces became much more essential in topology, with the development of computer science. The task of this paper is to study and investigate some properties of such spaces with the existence of an ordered relation between…
We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…
We introduce the o-minimal LS-category of definable sets in o-minimal expansions of ordered fields and we establish a relation with the semialgebraic and the classical one. We also study the o-minimal LS-category of definable groups. Along…
We consider definably complete and Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain can not be written as the union of a definable increasing family of nowhere dense…
It is known that monoidal categories have a finite definition, whereas multicategories have an infinite (albeit finitary) definition. Since monoidal categories correspond to representable multicategories, it goes without saying that…
This is a thesis that was defended in 2009 at Lomonosov Moscow State University. In Chapter 1: 1. It is proved that that the class of lower (Skolem) elementary functions is the set of all polynomial-bounded functions that can be obtained by…
We introduce the notions of triviality and order-triviality for global invariant types in an arbitrary first-order theory and show that they are well behaved in the NIP context. We show that these two notions agree for invariant global…