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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Large models of countable height

Author: Harvey Friedman
Journal: Trans. Amer. Math. Soc. 201 (1975), 227-239
MSC: Primary 02H05; Secondary 02K15
MathSciNet review: 0416903
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Abstract: Eery countable transitive model $ M$ of ZF (without choice) has an ordinal preserving extension satisfying ZF, of power $ { \sqsupset _{M \cap On}}$. An application to infinitary logic is given.

References [Enhancements On Off] (What's this?)

  • [1] J. Barwise, Infinitary logic and admissible sets, Doctoral Dissertation, Stanford University, Stanford, Calif., 1967.
  • [2] C. C. Chang, Some remarks on the model theory of infinitary languages, The Syntax and Semantics of Infinitary Languages, Lecture Notes in Math., vol. 72, Springer-Verlag, Berlin, 1968, p. 47. MR 0234827 (38:3141)
  • [3] M. Morley, Omitting classes of elements, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 265-273. MR 34 #1189. MR 0201305 (34:1189)

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Article copyright: © Copyright 1975 American Mathematical Society

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