Tomasz Rzepecki

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We generalise the main theorems from the paper The Borel cardinality of Lascar strong types by I. Kaplan, B. Miller and P. Simon to a wider class of bounded invariant equivalence relations. We apply them to describe relationships between fundamental properties of bounded invariant equivalence relations (such as smoothness or type-de nability) which also(More)
We develop topological dynamics for the group of automorphism of a monster model of any given theory. In particular, we nd strong relationships between objects from topological dynamics (such as the generalized Bohr compacti cation introduced by Glasner) and various Galois groups of the theory in question, obtaining essentially new information about them,(More)
We study, in an abstract context, equivalence relations which are invariant under group actions. More precisely, we fix a transformation group, and we study the orbital equivalence relations (i.e. orbit equivalence relations of normal subgroups) and a wider class of weakly orbital equivalence relations. For these sorts of relations we show (under some(More)