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Hanf number of omitting type for simple first-order theories

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Hebrew University, Jerusalem, Israel


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.

Research Article
Copyright © Association for Symbolic Logic 1979

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