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2009 Comparing Borel Reducibility and Depth of an ω-Stable Theory
Martin Koerwien
Notre Dame J. Formal Logic 50(4): 365-380 (2009). DOI: 10.1215/00294527-2009-016


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.


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Martin Koerwien . "Comparing Borel Reducibility and Depth of an ω-Stable Theory." Notre Dame J. Formal Logic 50 (4) 365 - 380, 2009.


Published: 2009
First available in Project Euclid: 11 February 2010

zbMATH: 1203.03045
MathSciNet: MR2598869
Digital Object Identifier: 10.1215/00294527-2009-016

Primary: 03C15 , 03C45 , 03E15

Keywords: Borel reducibility , classifications , countable models , omega-stability

Rights: Copyright © 2009 University of Notre Dame


Vol.50 • No. 4 • 2009
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