On Automorphism Groups of Countable Structures
colorful horizontal rule

Su Gao

Abstract

Strengthening a theorem of D.W. Kueker, this paper completely characterizes which countable structures do not admit uncountable L1-elementarily equivalent models. In particular, it is shown that if the automorphism group of a countable structure M is abelian, or even just solvable, then there is no uncountable model of the Scott sentence of M. These results arise as part of a study of Polish gourps with compatible left-invariant complete metrics.

Table of Contents

  1. Introduction
  2. Polish Groups with Compatible Left-Invariant Complete Metrics
  3. The Main Result
    References
This paper was published in The Journal of Symbolic Logic 63 (1998), 891-896.

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