Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Representing projective sets as unions of Borel sets


Author: Howard Becker
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] H. Becker, AD and the supercompactness of $ {\aleph _1}$, J. Symbolic Logic 46 (1981), 822-842. MR 641495 (83b:03061)
  • [2] -, The restriction of a Borel equivalence relation to a sparse set, in preparation.
  • [3] L. Harrington, Analytic determinacy and $ {0^\char93 }$, J. Symbolic Logic 43 (1978), 685-694. MR 518675 (80b:03065)
  • [4] L. A. Harrington, A. S. Kechris, and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc. 3 (1990), 903-928. MR 1057041 (91h:28023)
  • [5] A. S. Kechris, The structure of Borel equivalence relations in Polish spaces, Set Theory of the Continuum (H. Judah, W. Just, and H. Woodin, eds.), Math. Sci. Res. Inst. Publ., vol. 26, Springer-Verlag, New York, 1992, pp. 89-102. MR 1233813 (94h:03093)
  • [6] A. S. Kechris, R. M. Solovay, and J. R. Steel, The axiom of determinacy and the prewellordering property, Cabal Seminar 77-79 (A. S. Kechris, D. A. Martin, and Y. N. Moschovakis, eds.), Lecture Notes in Math., vol. 839, Springer-Verlag, New York, 1981, pp. 101-125. MR 611169 (83f:03042)
  • [7] A. S. Kechris and W. H. Woodin, Generic codes for uncountable ordinals, partition properties and elementary embeddings, xeroxed notes, 1980.
  • [8] Y. N. Moschovakis, Descriptive set theory, North-Holland, Amsterdam, 1980. MR 561709 (82e:03002)
  • [9] W. H. Woodin, AD and the uniqueness of the supercompact measures on $ {P_{{\omega _1}}}(\lambda )$, Cabal Seminar 79-81 (A. S. Kechris, D. A. Martin, and Y. N. Moschovakis, eds.), Lecture Notes in Math., vol. 1019, Springer-Verlag, New York, 1983, pp. 67-71. MR 730587

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E15, 03E60

Retrieve articles in all journals with MSC: 03E15, 03E60


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1224612-9
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society