Stability and omitting types

Ehud Hrushovski; Saharon Shelah

doi:10.1007/BF02775793

Stability and omitting types

Ehud Hrushovski^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 2^א₀; 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 2^א₀, and this is sharp. Several improvements and some negative results are listed in the introduction.

Original language	English
Pages (from-to)	289-321
Number of pages	33
Journal	Israel Journal of Mathematics
Volume	74
Issue number	2-3
DOIs	https://doi.org/10.1007/BF02775793
State	Published - Oct 1991

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title = "Stability and omitting types",

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.",

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AB - 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.

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Stability and omitting types

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