Journal of Symbolic Logic

A complicated ω-stable depth 2 theory

Martin Koerwien

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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.

Article information

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

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1294170989

Digital Object Identifier
doi:10.2178/jsl/1294170989

Mathematical Reviews number (MathSciNet)
MR2791337

Zentralblatt MATH identifier
1215.03052

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

Keywords
omega-stability classification countable models Borel reducibility Scott height

Citation

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


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