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Hanf number of omitting type for simple first-order theories
Journal of Symbolic Logic 44 (3):319-324 (1979)
Abstract
Let T be a complete countable first-order theory such that every ultrapower of a model of T is saturated. If T has a model omitting a type p in every cardinality $ then T has a model omitting p in every cardinality. There is also a related theorem, and an example showing the $\beth_\omega$ cannot be improvedLinks
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References found in this work
Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory.Saharon Shelah - 1971 - Annals of Mathematical Logic 3 (3):271-362.
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