Games of length $\omega \cdot 2$
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- by Benedikt Löwe and Philipp Rohde PDF
- Proc. Amer. Math. Soc. 130 (2002), 1247-1248 Request permission
Abstract:
This note combines an unpublished theorem of Woodin’s about $\mathsf {AD}$ and Uniformisation with combinatorial arguments of Blass’ to get a startling consequence for games on $\omega$ of length $\omega \cdot 2$: The determinacy of these games is equivalent to the Axiom of Real Determinacy.References
- Andreas Blass, Equivalence of two strong forms of determinacy, Proc. Amer. Math. Soc. 52 (1975), 373–376. MR 373903, DOI 10.1090/S0002-9939-1975-0373903-X
- Akihiro Kanamori, The higher infinite, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1994. Large cardinals in set theory from their beginnings. MR 1321144
- Jan Mycielski, On the axiom of determinateness, Fund. Math. 53 (1963/64), 205–224. MR 161787, DOI 10.4064/fm-53-2-205-224
- Ernst Zermelo, Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, in: E. W. Hobson, A. E. H. Love (eds.), Proceedings of the Fifth International Congress of Mathematicians, Cambridge 1912, Volume 2, Cambridge 1913, p. 501–504
Additional Information
- Benedikt Löwe
- Affiliation: Mathematisches Institut, Rheinische Friedrich–Wilhelms–Universität Bonn, Beringstraße 6, 53115 Bonn, Germany
- Email: loewe@math.uni-bonn.de
- Philipp Rohde
- Affiliation: Mathematisches Institut, Rheinische Friedrich–Wilhelms–Universität Bonn, Beringstraße 6, 53115 Bonn, Germany
- Email: rohde@math.uni-bonn.de
- Received by editor(s): April 2, 2001
- Received by editor(s) in revised form: May 2, 2001
- Published electronically: November 9, 2001
- Additional Notes: The authors would like to thank the anonymous referee for encouraging suggestions that led to a considerable improvement in the exposition.
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1247-1248
- MSC (2000): Primary 03E60, 03E25, 03E35, 03E45
- DOI: https://doi.org/10.1090/S0002-9939-01-06407-3
- MathSciNet review: 1873804