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June 2005 Finitely axiomatizable ω-categorical theories and the Mazoyer hypothesis
David Lippel
J. Symbolic Logic 70(2): 460-472 (June 2005). DOI: 10.2178/jsl/1120224723

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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David Lippel. "Finitely axiomatizable ω-categorical theories and the Mazoyer hypothesis." J. Symbolic Logic 70 (2) 460 - 472, June 2005. https://doi.org/10.2178/jsl/1120224723

Information

Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1084.03029
MathSciNet: MR2140041
Digital Object Identifier: 10.2178/jsl/1120224723

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 2 • June 2005
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