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- Manuel Bodirsky, Michael Pinsker, Todor Tsankov
- 2011 IEEE 26th Annual Symposium on Logic in…
- 2011

For a fixed infinite structure $\Gamma$ with finite signature tau, we study the following computational problem: input are quantifier-free first-order tau-formulas phi_0,phi_1,...,phi_n that define relations R_0,R_1,\dots,R_n over Gamma. The question is whether the relation R_0 is primitive positive definable from R_1,...,R_n, i.e., definable by a… (More)

In this paper, we study the connections between properties of the action of a countable group Γ on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of Γ on MX , where M is a measure space. In particular, we show that the action of Γ on X is amenable iff the shift Γ… (More)

We study full groups of countable, measure-preserving equivalence relations. Our main results include that they are all homeomorphic to the separable Hilbert space and that every homomorphism from an ergodic full group to a separable group is continuous. We also find bounds for the minimal number of topological generators (elements generating a dense… (More)

- Todor Tsankov
- J. Symb. Log.
- 2011

We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are p-divisible for infinitely many primes p, or groups of the form L p∈I Z(p ), where I is an infinite set of primes.

- Todor Tsankov
- 2008

Consider a standard probability space (X,μ), i.e., a space isomorphic to the unit interval with Lebesgue measure. We denote by Aut(X,μ) the automorphism group of (X,μ), i.e., the group of all Borel automorphisms of X which preserve μ (where two such automorphisms are identified if they are equal μ-a.e.). A Borel equivalence relation E ⊆ X is called… (More)

If G is a Polish group and Γ is a countable group, denote byHom(Γ,G) the space of all homomorphisms Γ → G. We study properties of the group π(Γ) for the generic π ∈ Hom(Γ,G), when Γ is abelian and G is one of the following three groups: the unitary group of an infinite-dimensional Hilbert space, the automorphism group of a standard probability space, and… (More)

We prove that if the universalminimal flow of a Polish groupG ismetrizable and contains a Gδ orbit G · x0, then it is isomorphic to the completion of the homogeneous space G/Gx0 and show how this result translates naturally in terms of structural Ramsey theory. We also investigate universal minimal proximal flows and describe concrete representations of… (More)

Consider a measure-preserving action Γ y (X,μ) of a countable group Γ and a measurable cocycle α : X × Γ → Aut(Y ) with countable image, where (X,μ) is a standard Lebesgue space and (Y, ν) is any probability space. We prove that if the Koopman representation associated to the action Γ y X is non-amenable, then there does not exist a countable-to-one Borel… (More)

- Itäı Ben Yaacov, Todor Tsankov, Ben Yaacov
- 2017

We investigate the automorphism groups of א0-categorical structures and prove that they are exactly the Roelcke precompact Polish groups. We show that the theory of a structure is stable if and only if every Roelcke uniformly continuous function on the automorphism group is weakly almost periodic. Analysing the semigroup structure on the weakly almost… (More)

- Todor Tsankov
- 2013

We develop Fraïssé theory, namely the theory of Fraïssé classes and Fraïssé limits, in the context of metric structures. We show that a class of finitely generated structures is Fraïssé if and only if it is the age of a separable approximately homogeneous structure, and conversely, that this structure is necessarily the unique limit of the class, and is… (More)