Model-theoretic characterizations of arcs and simple closed curves

Author:

Bankston Paul

Abstract

Two compact Hausdorff spaces are co-elementarily equivalent if they have homeomorphic ultracopowers; equivalently if their Banach spaces of continuous real-valued functions have isometrically isomorphic Banach ultrapowers (or, approximately satisfy the same positive-bounded sentences). We prove here that any locally connected compact metrizable space co-elementarily equivalent with an arc (resp. a simple closed curve) is itself an arc (resp. a simple closed curve). The hypotheses of metrizability and local connectedness cannot be dropped.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference12 articles.

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5. \bysame, Taxonomies of model-theoretically defined topological properties (submitted).

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1. The Chang-Łoś-Suszko theorem in a topological setting;Archive for Mathematical Logic;2005-03-14

2. Some Applications of the Ultrapower Theorem to the Theory of Compacta;Papers in Honour of Bernhard Banaschewski;2000

3. A hierarchy of maps between compacta;Journal of Symbolic Logic;1999-12

4. Co-elementary equivalence for compact Hausdorff spaces and compact abelian groups;Journal of Pure and Applied Algebra;1990-11

5. Taxonomies of model-theoretically defined topological properties;Journal of Symbolic Logic;1990-06

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