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Finitely axiomatizable ω-categorical theories and the Mazoyer hypothesis

Published online by Cambridge University Press:  12 March 2014

David Lippel
David Lippel*
Affiliation:
Department of Mathematics., University of Notre Dame, Notre Dame. IN 46556-4618., USA, E-mail: [email protected]
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 460 - 472
Copyright
Copyright © Association for Symbolic Logic 2005

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