Stability and omitting types

Ehud Hrushovski*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We give a complete solution to the following question: when does a superstable theory have a model of power κ omitting a partial type q? In particular, for fixed q, if there is such a model of power א1 then there is one of power 2א 0; and if there is a model omitting q of power א1, then there are arbitrarily large ones. For stable theories, a model of power Beth{hebrew} ω +, omitting q implies one of power 2א 0, and this is sharp. Several improvements and some negative results are listed in the introduction.

Original languageEnglish
Pages (from-to)289-321
Number of pages33
JournalIsrael Journal of Mathematics
Volume74
Issue number2-3
DOIs
StatePublished - Oct 1991

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