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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Large models of countable height
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by Harvey Friedman PDF
Trans. Amer. Math. Soc. 201 (1975), 227-239 Request permission

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
    J. Barwise, Infinitary logic and admissible sets, Doctoral Dissertation, Stanford University, Stanford, Calif., 1967.
  • Jon Barwise (ed.), The syntax and semantics of infinitary languages, Lecture Notes in Mathematics, No. 72, Springer-Verlag, Berlin-New York, 1968. MR 0234827
  • Michael Morley, Omitting classes of elements, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 265–273. MR 0201305
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 201 (1975), 227-239
  • MSC: Primary 02H05; Secondary 02K15
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0416903-8
  • MathSciNet review: 0416903