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End extensions and numbers of countable models

  • Saharon Shelah (a1)

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.

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[G2] H. Gaifman , Uniform extension operators for models and their applications, Sets, models and recursion theory ( Crossley , Editor), North-Holland, Amsterdam, 1967, pp. 122155.

[K1] H.J. Keisler , Some model theoretic results on ω-logic, Israel Journal of Mathematics, vol. 4 (1966), pp. 249261.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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