Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Games of length $\omega\cdot 2$


Authors: Benedikt Löwe and Philipp Rohde
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
Published electronically: November 9, 2001
MathSciNet review: 1873804
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This note combines an unpublished theorem of Woodin's about $\mathsf{AD}$ and Uniformisation with combinatorial arguments of Blass' to get a startling consequence for games on $\omega$of length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 [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E60, 03E25, 03E35, 03E45

Retrieve articles in all journals with MSC (2000): 03E60, 03E25, 03E35, 03E45


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: https://doi.org/10.1090/S0002-9939-01-06407-3
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.
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society