Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-12T22:42:12.073Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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