A complicated ω-stable depth 2 theory

Journal of Symbolic Logic 76 (1):47 - 65 (2011)
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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

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Citations of this work

A descriptive Main Gap Theorem.Francesco Mangraviti & Luca Motto Ros - 2020 - Journal of Mathematical Logic 21 (1):2050025.

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References found in this work

Countable borel equivalence relations.S. Jackson, A. S. Kechris & A. Louveau - 2002 - Journal of Mathematical Logic 2 (01):1-80.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
New dichotomies for borel equivalence relations.Greg Hjorth & Alexander S. Kechris - 1997 - Bulletin of Symbolic Logic 3 (3):329-346.

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