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Preprint Number 264

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264. Ludomir Newelski
Model theoretic aspects of the Ellis semigroup

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Let G be a group definable in a theory T. For every model M of T, the space S_G(M) of the complete G-types over M is a G^M-flow. We compare the Ellis semigroups related to the flows S_G(M) and S_G(N) when M \prec N, focusing particularly on the groups into which the minimal left ideals in these semigroups split. In the case where T is an o-minimal expansion of the theory of reals and G is definably compact we show that these groups are isomorphic to the quotient group G/G^{00}.

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