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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Omitting types: application to descriptive set theory
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by Richard Mansfield PDF
Proc. Amer. Math. Soc. 47 (1975), 198-200 Request permission

Abstract:

The omitting types theorem of infinitary logic is used to prove that every small $\Pi _1^1$ set of analysis or any small ${\Sigma _1}$ set of set theory is constructible.
References
  • Kurt Gödel, The Consistency of the Continuum Hypothesis, Annals of Mathematics Studies, No. 3, Princeton University Press, Princeton, N. J., 1940. MR 0002514
  • Thomas J. Grilliot, Omitting types: application to recursion theory, J. Symbolic Logic 37 (1972), 81–89. MR 344099, DOI 10.2307/2272549
  • 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
  • Richard Mansfield, Perfect subsets of definable sets of real numbers, Pacific J. Math. 35 (1970), 451–457. MR 280380
  • Robert M. Solovay, On the cardinality of $\sum _{2}^{1}$ sets of reals, Foundations of Mathematics (Symposium Commemorating Kurt Gödel, Columbus, Ohio, 1966) Springer, New York, 1969, pp. 58–73. MR 0277382
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 47 (1975), 198-200
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0354371-0
  • MathSciNet review: 0354371