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Omitting types: application to descriptive set theory


Author: Richard Mansfield
Journal: Proc. Amer. Math. Soc. 47 (1975), 198-200
MathSciNet review: 0354371
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Abstract | References | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Kurt Gödel, The Consistency of the Continuum Hypothesis, Annals of Mathematics Studies, no. 3, Princeton University Press, Princeton, N. J., 1940. MR 0002514
  • [2] Thomas J. Grilliot, Omitting types: application to recursion theory, J. Symbolic Logic 37 (1972), 81–89. MR 0344099
  • [3] H. Jerome Keisler, Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers, North-Holland Publishing Co., Amsterdam-London, 1971. Studies in Logic and the Foundations of Mathematics, Vol. 62. MR 0344115
  • [4] Richard Mansfield, Perfect subsets of definable sets of real numbers, Pacific J. Math. 35 (1970), 451–457. MR 0280380
  • [5] Robert M. Solovay, On the cardinality of ∑₂¹ sets of reals, Foundations of Mathematics (Symposium Commemorating Kurt Gödel, Columbus, Ohio, 1966) Springer, New York, 1969, pp. 58–73. MR 0277382


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0354371-0
Keywords: Constructible, perfect set, hyperarithmetic, analytic
Article copyright: © Copyright 1975 American Mathematical Society