Polish group actions: Dichotomies and generalized elementary embeddings

Author:

Becker Howard

Abstract

We prove that any Polish group which admits a complete left-invariant metric satisfies the Topological Vaught Conjecture. We also generalize some theorems of model theory from the logic actions to other Polish group actions.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference46 articles.

1. Perspectives in Mathematical Logic;Barwise, Jon,1975

2. The topological Vaught’s conjecture and minimal counterexamples;Becker, Howard;J. Symbolic Logic,1994

3. \bysame, The number of path-components of a compact subset of ℝⁿ, Logic Colloquium 95 (J. A. Makowsky and E. V. Ravve, eds.), Lecture Notes in Logic, vol. 11, Springer-Verlag, to appear.

4. \bysame, Polish group actions and generalized model theory, in preparation.

5. H. Becker and R. Dougherty, On disjoint Borel uniformizations, Advances in Mathematics, to appear.

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