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End extensions and numbers of countable models

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Hebrew University, Jerusalem, Israel


We prove that every model of T = Th(ω, <,…) (T countable) has an end extension; and that every countable theory with an infinite order and Skolem functions has nonisomorphic countable models; and that if every model of T has an end extension, then every ∣T∣-universal model of T has an end extension definable with parameters.

Research Article
Copyright © Association for Symbolic Logic 1978

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