Related papers: On closed unbounded sets consisting of former regu…

We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…

We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…

We show that many countable support iterations of proper forcings preserve Souslin trees. We establish sufficient conditions in terms of games and we draw connections to other preservation properties. We present a proof of preservation…

A model with a sequence of indiscernibles depending on a particular precovering set is constructed.The initial assumption is as follows: for every n<omega the set {alpha | o(alpha)=alpha^+n } is unbounded in kappa.

Let $A \subset \mathbb{Z}^d$ be a finite set. It is known that the sumset $NA$ has predictable size ($\vert NA\vert = P_A(N)$ for some $P_A(X) \in \mathbb{Q}[X]$) and structure (all of the lattice points in some finite cone other than all…

Every bounded definable open set is a union of finitely many open strong cells in a weakly o-minimal expansion of a real closed field. We prove this fact and another theorem similar to it.

We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with…

We establish a sufficient condition for a finitely generated pro-$p$ group to be accessible in terms of finite generation of the module of ends.

We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…

We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.

A necessary and sufficient condition for an element of an algebra (in the sense of Universal Algebra) to be in the dominion of a subalgebra is given, in terms of transferable sets. This criterion is then used to formulate a more wieldy…

We consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index, and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractible…

We show that if the maximum modulus of a quasiregular mapping f grows sufficiently rapidly then there exists a non-empty escaping set I(f) consisting of points whose forward orbits under iteration tend to infinity. This set I(f) has an…

Predictive constructions are a powerful way of characterizing the probability law of stochastic processes with certain forms of invariance, such as exchangeability or Markov exchangeability. When de Finetti-like representation theorems are…

We prove that the complement of a closed set S satisfying an extended exterior sphere condition is nothing but the union of closed balls with common radius. This generalizes [11, Theorem 3] where the set S is assumed to be prox-regular, a…

We introduce a new method for building models of CH, together with $\Pi_2$ statements over $H(\omega_2)$, by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only $\aleph_1$-many of…

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…

We consider the problem of finding a condition for a univariate polynomial having a given multiplicity structure when the number of distinct roots is given. It is well known that such conditions can be written as conjunctions of several…

We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…

We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…