Journal of Symbolic Logic

Model theory without choice? Categoricity

Saharon Shelan

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

First available in Project Euclid: 2 June 2009

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

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