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The Strength of Blackwell determinacy

Published online by Cambridge University Press:  12 March 2014

Donald A. Martin ,
Itay Neeman  and
Marco Vervoort
Donald A. Martin
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095-1555, USA, E-mail: dam@math.ucla.edu
Itay Neeman
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095-1555, USA, E-mail: ineeman@math.ucla.edu
Marco Vervoort
Affiliation:
Faculty of Science, University of Amsterdam, Amsterdam, The Netherlands, E-mail: vervoort@science.uva.nl
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Abstract

We show that Blackwell determinacy in L(ℝ) implies determinacy in L(ℝ).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 2 , June 2003 , pp. 615 - 636
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[Kec95]Kechris, Alexander, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, 1995.CrossRefGoogle Scholar
[KS85]Kechris, Alexander and Solovay, Robert, On the relative consistency strength of determinacy hypothesis, Transactions of the American Mathematical Society, vol. 290 (1985), pp. 179–211.Google Scholar
[K.W83]Kechris, Alexander and Woodin, Hugh, Equivalence of partition properties and determinacy, Proceedings of the National Academy of Sciences USA, vol. 80 (1983), pp. 1783–1786.CrossRefGoogle Scholar
[Loe01]Loewe, Benedikt, Blackwell Determinacy, Ph.D. thesis, Humboldt–Universität zu Berlin, 2001.Google Scholar
[Mar98]Martin, Donald A., The Determinacy of Blackwell games, this Journal, vol. 63 (1998), pp. 1565–1582.Google Scholar
[Mos80]Moschovakis, Yiannis N., Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland, Amsterdam, 1980.Google Scholar
[Ste83]Steel, John, Scales in L[ℝ], Cabal seminar 1979–81, Lecture Notes in Mathematics, vol. 1019, Springer, 1983, pp. 107–156.Google Scholar
[Ver96]Vervoort, Marco, Blackwell games, Statistics, probability, and game theory: Papers in honor of David Blackwell (Ferguson, T.S., Shapley, L.S., and MacQueen, J.B., editors), Institute of Mathematical Statistics, 1996, pp. 369–390.CrossRefGoogle Scholar
[Ver00]Vervoort, Marco, Games, walks and grammars: Problems I've worked on, Ph.D. thesis, Universiteit van Amsterdam, 2000.Google Scholar