The Journal of Symbolic Logic

Research Article

End extensions and numbers of countable models

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.

(Received November 01 1976)