Representing projective sets as unions of Borel sets
HTML articles powered by AMS MathViewer
- by Howard Becker PDF
- Proc. Amer. Math. Soc. 123 (1995), 883-886 Request permission
Abstract:
We consider a method of representing projective sets by a particular type of union of Borel sets, assuming AD. We prove a generalization of the theorem that a set is $\sum _2^1$ iff it is the union of ${\omega _1}$ Borel sets.References
- Howard Becker, $\textrm {AD}$ and the supercompactness of $\aleph _{1}$, J. Symbolic Logic 46 (1981), no. 4, 822–842. MR 641495, DOI 10.2307/2273231 —, The restriction of a Borel equivalence relation to a sparse set, in preparation.
- Leo Harrington, Analytic determinacy and $0^{\sharp }$, J. Symbolic Logic 43 (1978), no. 4, 685–693. MR 518675, DOI 10.2307/2273508
- L. A. Harrington, A. S. Kechris, and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc. 3 (1990), no. 4, 903–928. MR 1057041, DOI 10.1090/S0894-0347-1990-1057041-5
- Alexander S. Kechris, The structure of Borel equivalence relations in Polish spaces, Set theory of the continuum (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 26, Springer, New York, 1992, pp. 89–102. MR 1233813, DOI 10.1007/978-1-4613-9754-0_{7}
- Alexander S. Kechris, Robert M. Solovay, and John R. Steel, The axiom of determinacy and the prewellordering property, Cabal Seminar 77–79 (Proc. Caltech-UCLA Logic Sem., 1977–79) Lecture Notes in Math., vol. 839, Springer, Berlin-New York, 1981, pp. 101–125. MR 611169 A. S. Kechris and W. H. Woodin, Generic codes for uncountable ordinals, partition properties and elementary embeddings, xeroxed notes, 1980.
- Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 561709
- W. Hugh Woodin, $\textrm {AD}$ and the uniqueness of the supercompact measures on $P\omega _{1}(\lambda )$, Cabal seminar 79–81, Lecture Notes in Math., vol. 1019, Springer, Berlin, 1983, pp. 67–71. MR 730587, DOI 10.1007/BFb0071694
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 883-886
- MSC: Primary 03E15; Secondary 03E60
- DOI: https://doi.org/10.1090/S0002-9939-1995-1224612-9
- MathSciNet review: 1224612