Finitely Axiomatizable ω-Categorical Theories and the Mazoyer Hypothesis

Journal of Symbolic Logic 70 (2):460 - 472 (2005)
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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DOI 10.2178/jsl/1120224723
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Alexandre A. Ivanov & Dugald Macpherson (1999). Strongly Determined Types. Annals of Pure and Applied Logic 99 (1-3):197-230.

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