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Borel Complexity Of The Isomorphism Relation For O-Minimal Theories, Davender Singh Sahota '99

Doctoral Dissertations

In 1988, Mayer published a strong form of Vaught's Conjecture for o-minimal theories (1). She showed Vaught's Conjecture holds, and characterized the number of countable models of an o-minimal theory T if T has fewer than 2K ° countable models. Friedman and Stanley have shown in (2) that several elementary classes are Borel complete. This work addresses the class of countable models of an o-minimal theory T when T has 2N ° countable models, including conditions for when this class is Borel complete. The main result is as follows.

Theorem 1. Let T be an o-minimal theory in a countable …