Hanf number of omitting type for simple first-order theories

Publisher： Cambridge University Press

E-ISSN： 1943-5886|44|3|319-324

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.44, Iss.3, 1979-09, pp. : 319-324

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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 < ℶ′, then T has a model omitting p in every cardinality. There is also a related theorem, and an example showing the ℶ′ cannot be improved.

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