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Journals and Conferences
Let G be a closed subgroup of S∞ and X be a Polish G-space with a countable basisA of clopen sets. Each x ∈ X defines a characteristic function τx on A by τx(A) = 1 ⇔ x ∈ A. We consider computable complexity of τx and some related questions.
Let G be an uncountable universal locally finite group. We study subgroups H < G such that for every g ∈ G, |H : H ∩H| < |H|.
Let G be a non-trivial algebraically closed group and X be a subset of G generating G in infinitely many steps. We give a construction of a binary tree associated with (G,X). Using this we show that if G is ω1-existentially closed then it is strongly bounded.
We generalize some model theory involving Hyp(M) and HF(M) to the case of actions of Polish groups on Polish spaces. In particular we obtain two variants of the Nadel’s theorem about relationships between Scott sentences and admissible sets.