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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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An $L_{\omega _{1}\omega }$ complete and consistent theory without models
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by M. Makkai and J. Mycielski
Proc. Amer. Math. Soc. 62 (1977), 131-133
DOI: https://doi.org/10.1090/S0002-9939-1977-0439578-8

Abstract:

We simplify the example of Ryll-Nardzewski of an ${L_{{\omega _1}\;\omega }}$ theory with the above properties. We include other facts on the relationship of logic to 01-laws and on the ${L_{{\omega _1}\;\omega }}$ definability of some sets which are meager but of full measure.
References
  • Dana Scott, Logic with denumerably long formulas and finite strings of quantifiers, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 329–341. MR 0200133
  • H. Jerome Keisler, Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers, Studies in Logic and the Foundations of Mathematics, Vol. 62, North-Holland Publishing Co., Amsterdam-London, 1971. MR 0344115
  • J. Mycielski, Measure and category of some sets of models, Notices Amer. Math. Soc. 22 (1975), A-475-A-476. Abstract 75T-E43.
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Bibliographic Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 62 (1977), 131-133
  • MSC: Primary 02B25
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0439578-8
  • MathSciNet review: 0439578