Journal of Symbolic Logic

Model theory without choice? Categoricity

Saharon Shelan

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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).

Article information

Source
J. Symbolic Logic, Volume 74, Issue 2 (2009), 361-401.

Dates
First available in Project Euclid: 2 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1243948319

Digital Object Identifier
doi:10.2178/jsl/1243948319

Mathematical Reviews number (MathSciNet)
MR2518563

Citation

Shelan, Saharon. Model theory without choice? Categoricity. J. Symbolic Logic 74 (2009), no. 2, 361--401. doi:10.2178/jsl/1243948319. https://projecteuclid.org/euclid.jsl/1243948319


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