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We generalise the main theorems from the paper The Borel car-dinality 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-denability) 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 com-pactication introduced by Glasner) and various Galois groups of the theory in question, obtaining essentially new information about them,(More)