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Analytic sets from the point of view of compact sets

Published online by Cambridge University Press:  24 October 2008

Howard Becker
Howard Becker
Affiliation:
Department of Mathematics and Statistics, University of South Carolina, Columbia, SC 29208, U.S.A., and Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, U.S.A.
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Extract

A set A ⊂ ωω is called compactly if, for every compact K ⊂ ωω, A ∩ K is . Consider the proposition that every compactly set is . (AD implies that it is true, ZFC + CH implies that it is false.) We are concerned here with whether this is consistent with ZFC, particularly when n = 1. In the case of sets (that is, analytic sets), this consistency question is due to Fremlin (see [7], page 483, problem 18). Kunen and Miller [3] have proved the following two theorems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 1 - 4
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Hechler, S. H.. On the existence of certain cofinal subsets of ωω. Proc. of Symp. in Pure Math., 13 (2) (1974), 155–173.CrossRefGoogle Scholar
[2]Kechris, A. S.. Homogeneous trees and projective scales Cabal Seminar 77–79, Lecture Notes in Math., vol. 839 (Springer-Verlag, 1981), 33–74.CrossRefGoogle Scholar
[3]Kunen, K. and Miller, A. W.. Borel and projective sets from the point of view of compactsets. Math. Proc. Cambridge Philos. Soc. 94 (1983), 399–409.CrossRefGoogle Scholar
[4]Martin, D. A.. Borel and Projective Games, to appear.Google Scholar
[5]Martin, D. A. and Solovay, R. M.. A basis theorem for sets of reals. Ann of Math. 89 (1969), 138–160.CrossRefGoogle Scholar
[6]Moschovakis, Y. N.. Descriptive Set Theory (North-Holland, 1980).Google Scholar
[7]Rogers, C. A. et al. Analytic Sets (Academic Press, 1980).Google Scholar