Journal of Symbolic Logic

A complicated ω-stable depth 2 theory

Martin Koerwien

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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.

Article information

J. Symbolic Logic, Volume 76, Issue 1 (2011), 47-65.

First available in Project Euclid: 4 January 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C15: Denumerable structures 03C45: Classification theory, stability and related concepts [See also 03C48] 03E15: Descriptive set theory [See also 28A05, 54H05]

omega-stability classification countable models Borel reducibility Scott height


Koerwien, Martin. A complicated ω-stable depth 2 theory. J. Symbolic Logic 76 (2011), no. 1, 47--65. doi:10.2178/jsl/1294170989.

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