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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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Generalized quantifiers and compact logic
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by Saharon Shelah
Trans. Amer. Math. Soc. 204 (1975), 342-364
DOI: https://doi.org/10.1090/S0002-9947-1975-0376334-6

Abstract:

We solve a problem of Friedman by showing the existence of a logic stronger than first-order logic even for countable models, but still satisfying the general compactness theorem, assuming e.g. the existence of a weakly compact cardinal. We also discuss several kinds of generalized quantifiers.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 204 (1975), 342-364
  • MSC: Primary 02H05; Secondary 02B20
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0376334-6
  • MathSciNet review: 0376334