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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the existence of $L_{\infty K}$-indiscernibles
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by P. C. Eklof
Proc. Amer. Math. Soc. 25 (1970), 798-800
DOI: https://doi.org/10.1090/S0002-9939-1970-0260579-0

Abstract:

It is proved that it $T$ is a countable theory of ${L_{{\omega _1}\omega }}$ with enough axioms for Skolem functions and with arbitrarily large models, then for any order type, there is a model of $T$ with a set of ${L_{\infty \kappa }}$-indiscernibles of that order type.
References
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  • C. C. Chang, “Some remarks on the model theory of infinitary languages,” The syntax and semantics of infinitary languages, Lecture Notes in Math., no. 72, Springer-Verlag, Berlin and New York, 1968, pp. 36-63.
  • C. C. Chang, Infinitary properties of models generated from indiscernibles, Logic, Methodology and Philos. Sci. III (Proc. Third Internat. Congr., Amsterdam, 1967) North-Holland, Amsterdam, 1968, pp. 9–21. MR 0250859
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  • J. Keisler, Model theory of ${L_{{\omega _1}\omega }}$, (to appear).
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 798-800
  • MSC: Primary 02.35
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0260579-0
  • MathSciNet review: 0260579