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A complicated ω-stable depth 2 theory

Published online by Cambridge University Press:  12 March 2014

Martin Koerwien
Martin Koerwien*
Affiliation:
Centre de Recerca Matematica, 08193 Bellaterra, Barcelona, Spain, E-mail: [email protected]
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Abstract

We present a countable complete first order theory T which is model theoretically very well behaved: it eliminates quantifiers, is ω-stable, it has NDOP and is shallow of depth two. On the other hand, there is no countable bound on the Scott heights of its countable models, which implies that the isomorphism relation for countable models is not Borel.

Keywords

03C1503C4503E15omega-stabilityclassificationcountable modelsBorel reducibilityScott height
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 47 - 65
Copyright
Copyright © Association for Symbolic Logic 2011

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