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Omitting types: application to descriptive set theory


Author: Richard Mansfield
Journal: Proc. Amer. Math. Soc. 47 (1975), 198-200
DOI: https://doi.org/10.1090/S0002-9939-1975-0354371-0
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] K. Gödel, The consistency of the continuum hypothesis, Ann. of Math. Studies, no. 3, Princeton Univ. Press, Princeton, N. J., 1940. MR 2, 66. MR 0002514 (2:66c)
  • [2] Thomas J. Grilliot, Omitting types: application to recursion theory, J. Symbolic Logic 37 (1972), 81-89. MR 0344099 (49:8839)
  • [3] H. J. Keisler, Model theory for infinitary logic, North-Holland, Amsterdam, 1971. MR 0344115 (49:8855)
  • [4] Richard Mansfield, Perfect subsets of definable sets of real numbers, Pacific J. Math. 35 (1970), 451-457. MR 43 #6100. MR 0280380 (43:6100)
  • [5] R. M. Solovay, On the cardinality of $ \Sigma _2^1$ sets of reals, Foundations of Math. (Sympos. Commemorating Kurt Gödel, Columbus, Ohio, 1966), Springer, New York, 1969, pp. 58-73. MR 43 #3115. MR 0277382 (43:3115)


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

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