Related papers: Computability of F{\o}lner sets

We prove some technical results on definable types in $p$-adically closed fields, with consequences for definable groups and definable topological spaces. First, the code of a definable $n$-type (in the field sort) can be taken to be a real…

We show that every countable group H with solvable word problem (=computable group) can be subnormally embedded into a 2-generated group G which also has solvable word problem. Moreover, the membership problem for H < G is also solvable. We…

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on…

In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an algorithm for constructing quadratics whose Julia sets are uncomputable. We also show that a filled Julia set of a…

Solovay proved that there exists a computable upper bound f of the prefix-free Kolmogorov complexity function K such that f (x) = K(x) for infinitely many x. In this paper, we consider the class of computable functions f such that K(x) <= f…

The satisfiability problem for multilevel syllogistic extended with the Cartesian product operator (MLSC) is a long-standing open problem in computable set theory. For long, it was not excluded that such a problem were undecidable, due to…

Let $G$ be a finite solvable group. Then $G$ always has a useful presentation, which we call a "long presentation". Using a "long presentation" of $G$, we present an inductive method of constructing the irreducible representations of $G$…

We introduce the subgroup identification problem, and show that there is a finitely presented group G for which it is unsolvable, and that it is uniformly solvable in the class of finitely presented locally Hopfian groups. This is done as…

Existentially closed groups are, informally, groups that contain solutions to every consistent finite system of equations and inequations. They were introduced in 1951 in an algebraic context and subsequent research elucidated deep…

We prove an analogue of the fixed-point theorem for the case of definably amenable groups.

We exhibit infinitely many natural numbers $n$ for which there exists at least one insolvable group of order $n$, and yet the holomorph of any solvable group of order $n$ has no insolvable regular subgroup. We also solve Problem 19.90 (d)…

Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…

In this paper, we introduce the notions of lowerable, D-lowerable, P-lowerable, hereditarily lowerable, and hereditarily uniformly lowerable for countably infinite amenable group actions. We show that a system with finite entropy is…

We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…

We study a family of groups consisting of the simplest extensions of lamplighter groups. We use these groups to answer multiple open questions in combinatorial group theory, providing groups that exhibit various combinations of properties:…

We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their…

Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees…

We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the n^(log_p n + O(1)) generator-enumeration algorithm. In previous work…

This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in $\mathrm{NIP}$ or $\mathrm{NTP_2}$ settings. An abstract theorem constructing definable group homomorphisms from…

We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…