Related papers: Polish group actions and computability

We show that locally solvable subgroups of PLo(I) are countable. Then for each countable ordered set, we construct a locally solvable subgroup of Thompson's Group F. We develop machinery for understanding embeddings from solvable subgroups…

We prove that every clone of operations on a finite set A, if it contains a Malcev operation, is finitely related -- i.e., identical with the clone of all operations respecting R for some finitary relation R over A. It follows that for a…

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…

We show that every essentially countable orbit equivalence relation induced by a continuous action of a Polish group on a Polish space is $\sigma$-lacunary. In combination with [Invent. Math.201 (1), 309-383, 2015] we obtain a…

Let $\Aut(G)$ denote the group of (bi-)continuous automorphisms %and $\Out(G)$ the outer automorphism group of a non-Archimedean Polish group~$G$. We show that for any such $G$ with an invariant countable basis of open subgroups, the group…

Guralnick, Kunyavskii, Plotkin and Shalev have shown that the solvable radical of a finite group $G$ can be characterized as the set of all $x\in G$ such that $<x,y>$ is solvable for all $y\in G$. We prove two generalizations of this…

Let G be an infinite discrete countable amenable group acting continuously on a Lebesgue space X. In this article, using partition and factor-space, the conditional entropy of the action G is defined. We introduction some properties of…

We define a class of functions termed "Computable in the Limit", based on the Machine Learning paradigm of "Identification in the Limit". A function is Computable in the Limit if it defines a property P_p of a recursively enumerable class A…

We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with…

We make further observations on the features of Galois cohomology in the general model theoretic context. We make explicit the connection between forms of definable groups and first cohomology sets with coefficients in a suitable…

Let $M=I$ or $M=\mathbb{S}^1$ and let $k\geq 1$. We exhibit a new infinite class of Polish groups by showing that each group $\mathop{\rm Diff}_+^{k+AC}(M)$, consisting of those $C^k$ diffeomorphisms whose $k$-th derivative is absolutely…

We investigate the behavior of functional countability and exponential separability in products and subspaces of topological spaces. We solve a problem of Tkachuk by showing that the product of functionally countable pseudocompact spaces is…

In this paper we develop a technique of constructing uni- formly continuous maps between function spaces Cp(X) endowed with the pointwise topology. We prove that if a space X is compact metrizable and strongly countable-dimensional, then…

We give new characterizations of sofic groups: -- A group $G$ is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups. -- A group $G$ is sofic if and only if any system of equations…

We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative $C^*$ algebras.

We define and study Poissonian actions of Polish groups as a framework to Poisson suspensions, characterize them spectrally, and provide a complete characterization of their ergodicity. We further construct 'spatial' Poissonian actions,…

We embed a countably categorical group G into a locally compact group c(G) with a non-trivial topology and study how topological properties of c(G) are connected with the structure of definable subgroups of G.

We study presentations of $C^*(X)$ that are evaluative over a presentation of $X$ in that $(f,p) \mapsto f(p)$ is computable. We prove existence-uniqueness theorems for such presentations. We use our methods to prove an effective…

It is known that a group G definable in the field of p-adic numbers is definably locally isomorphic to the group of Q_p-points of a connected algebraic group H defined over Q_p. We show that if H is commutative then G is…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…