Omitting types: application to descriptive set theory
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- by Richard Mansfield
- Proc. Amer. Math. Soc. 47 (1975), 198-200
- DOI: https://doi.org/10.1090/S0002-9939-1975-0354371-0
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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
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- 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
Bibliographic 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