Abstract We show that every countable group with infinite finite conjugacy (FC)-center has the Schmidt property, is, admits a free, ergodic, measure-preserving action on standard probability space such full of associated orbit equivalence relation contains non-trivial central sequence. As consequence, countable, inner amenable property (T) property.

This paper denes and investigates the ergodic proper-ties of the entropy of a countable partition of a fuzzy dynamical sys-tem at different points of the state space. It ultimately introducesthe local fuzzy entropy of a fuzzy dynamical system and proves itto be an isomorphism invariant.

Akbarov’s theory of holomorphic reflexivity for topological Hopf algebras has been developed in two directions, namely, by the complication definitions when expanding scope and their simplification restricting. In framework latter approach, we establish associated with locally finite countable groups second-countable profinite groups. Abelian case, is described terms close to classical ones.

Let P be a set of reals viewed as a mass problem, i.e., a “decision problem with more than one solution.” Here the “solutions” of P are the elements of P . Many unsolvable mathematical problems are best viewed as mass problems. One says that a mass problem P is weakly reducible to a mass problem Q if for every solution Y of Q there exists a solution X of P such that X is Turing reducible to Y ....

We present some applications of Popa’s Superrigidity Theorem to the theory of countable Borel equivalence relations. In particular, we show that the universal countable Borel equivalence relation E∞ is not essentially free.

We show that the automorphism group of the countable universal distributive lattice has strong uncountable cofinality, and we adapt the method to deduce the strong uncountable cofinality of the automorphism group of the countable universal generalized boolean algebra.

Examples of spaces X are constructed for which Cp(X) is not normal but all closed discrete subsets are countable. A monolithic example is constructed in ZFC and a separable first countable example is constructed using ♦.

We force a first countable, normal, locally compact, initially ω1-compact but non-compact space X of size ω2. The onepoint compactification of X is a non-first countable compactum without any (non-trivial) converging ω1-sequence.

In this paper we examine the structure of countable closed invariant sets under a dynamical system on a compact metric space. We are motivated by a desire to understand the possible structures of inhomogeneities in one-dimensional non-hyperbolic sets (inverse limits of finite graphs) particularly when those inhomogeneities form a countable set. All of the previous literature regarding the colle...

In the early days of the development of model theory it was considered natural and was certainly beneficial to assume that the theories under investigation were in a countable language. The primary advantage of this assumption was the presence of the Omitting Types Theorem of Grzegorczyk, Mostowski, and Ryll-Nardzewski [1], which generalized arguments of Henkin [3] and Orey [8]. Following this,...