Finitely Axiomatizable ω-categorical Theories and the Mazoyer Hypothesis

Document Type

Journal Article

Role

Author

Standard Number

0022-4812

Journal Title

Journal of Symbolic Logic

Volume

70

Issue

2

First Page

460

Last Page

472

Publication Date

2005

Abstract

Let F be the class of complete, finitely axiomatizable ω-categorical theories. It is not known whether there are simple theories in F. We prove three results of the form: if T ∈ F has a sufficently well-behaved definable set J, then T is not simple. (In one case, we actually prove that T has the strict order property.) All of our arguments assume that the definable set J satisfies the Mazoyer hypothesis, which controls how an element of J can be algebraic over a subset of the model. For every known example in F, there is a definable set satisfying the Mazoyer hypothesis

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