Notre Dame Journal of Formal Logic

Comparing Borel Reducibility and Depth of an ω-Stable Theory

Martin Koerwien

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Abstract

In "A proof of Vaught's conjecture for ω-stable theories," the notions of ENI-NDOP and eni-depth have been introduced, which are variants of the notions of NDOP and depth known from Shelah's classification theory. First, we show that for an ω-stable first-order complete theory, ENI-NDOP allows tree decompositions of countable models. Then we discuss the relationship between eni-depth and the complexity of the isomorphism relation for countable models of such a theory in terms of Borel reducibility as introduced by Friedman and Stanley and construct, in particular, a sequence of complete first-order ω-stable theories ( T α ) α < ω 1 with increasing and cofinal eni-depth and isomorphism relations which are strictly increasing with respect to Borel reducibility.

Article information

Source
Notre Dame J. Formal Logic, Volume 50, Number 4 (2009), 365-380.

Dates
First available in Project Euclid: 11 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1265899120

Digital Object Identifier
doi:10.1215/00294527-2009-016

Mathematical Reviews number (MathSciNet)
MR2598869

Zentralblatt MATH identifier
1203.03045

Subjects
Primary: 03C15 03C45 03E15

Keywords
omega-stability classifications countable models Borel reducibility

Citation

Koerwien , Martin. Comparing Borel Reducibility and Depth of an ω-Stable Theory. Notre Dame J. Formal Logic 50 (2009), no. 4, 365--380. doi:10.1215/00294527-2009-016. https://projecteuclid.org/euclid.ndjfl/1265899120


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