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Games of length $\omega\cdot 2$

Author(s): Benedikt Löwe; Philipp Rohde
Journal: Proc. Amer. Math. Soc. 130 (2002), 1247-1248.
MSC (2000): Primary 03E60, 03E25, 03E35, 03E45
Posted: November 9, 2001
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Abstract: This note combines an unpublished theorem of Woodin's about $\mathsf{AD}$ and Uniformisation with combinatorial arguments of Blass' to get a startling consequence for games on $\omega$of length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:

[Bl75]
Andreas Blass, Equivalence of Two Strong Forms of Determinacy, Proceedings of the American Mathematical Society 52 (1975), p. 373-376 MR 51:10103

[Ka94]
Akihiro Kanamori, The Higher Infinite, Large Cardinals in Set Theory from Their Beginnings, Berlin 1994 [Perspectives in Mathematical Logic] MR 96k:03125

[My63]
Jan Mycielski, On the Axiom of Determinateness I, Fundamenta Mathematicae 53 (1963), p. 205-224 MR 28:4991

[Zer13]
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

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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

DOI: 10.1090/S0002-9939-01-06407-3
PII: S 0002-9939(01)06407-3
Received by editor(s): April 2, 2001
Received by editor(s) in revised form: May 2, 2001
Posted: 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 of article: Copyright 2001, American Mathematical Society

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