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 language | English |
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Pages (from-to) | 289-321 |
Number of pages | 33 |
Journal | Israel Journal of Mathematics |
Volume | 74 |
Issue number | 2-3 |
DOIs | |
State | Published - Oct 1991 |