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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the commutativity of ultraproducts with direct products
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by Michel Hébert PDF
Proc. Amer. Math. Soc. 113 (1991), 213-216 Request permission

Abstract:

We show that an ultraproduct of direct products of structures is elementarily equivalent to a direct product (naturally defined over an ultraproduct of sets!) of ultraproducts of these structures.
References
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  • S. Feferman and R. L. Vaught, The first order properties of products of algebraic systems, Fund. Math. 47 (1959), 57–103. MR 108455, DOI 10.4064/fm-47-1-57-103
  • Michel Hébert, Preservation and interpolation through binary relations between theories, Z. Math. Logik Grundlag. Math. 35 (1989), no. 2, 169–182. MR 992191, DOI 10.1002/malq.19890350206
  • M. Makkai, A compactness result concerning direct products of models, Fund. Math. 57 (1965), 313–325. MR 188071, DOI 10.4064/fm-57-3-313-325
  • R. L. Vaught, On sentences holding in direct products of relational systems, Proc. Internat. Congr. Math., vol. 2, Amsterdam, 1954. Y. Vourtsanis, The structure of truth in products of structures, preprint, Bowling Green State Univ., 1988.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 213-216
  • MSC: Primary 03C20; Secondary 03C40
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1086582-2
  • MathSciNet review: 1086582