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June 2009 Model theory without choice? Categoricity
Saharon Shelan
J. Symbolic Logic 74(2): 361-401 (June 2009). DOI: 10.2178/jsl/1243948319

Abstract

We prove łos conjecture=Morley theorem in ZF, with the same characterization, i.e., of first order countable theories categorical in ℵα for some (equivalently for every ordinal) α > 0. Another central result here in this context is: the number of models of a countable first order T of cardinality ℵα is either ≥ |α| for every α or it has a small upper bound (independent of α close to ℶ2).

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Saharon Shelan. "Model theory without choice? Categoricity." J. Symbolic Logic 74 (2) 361 - 401, June 2009. https://doi.org/10.2178/jsl/1243948319

Information

Published: June 2009
First available in Project Euclid: 2 June 2009

MathSciNet: MR2518563
Digital Object Identifier: 10.2178/jsl/1243948319

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 2 • June 2009
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