Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T03:03:36.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Determinacy for games ending at the first admissible relative to the play

Published online by Cambridge University Press:  12 March 2014

Itay Neeman
Itay Neeman*
Affiliation:
University of CaliforniaLos Angeles, Department of Mathematics, Los Angeles, CA 90095-1555, USA. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Let o(k) denote the Mitchell order of k. We show how to reduce long games which run to the first ordinal admissible in the play, to iteration games on models with a cardinal k so that (1) k is a limit of Woodin cardinals: and (2) o(k) = k++. We use the reduction to derive several optimal determinacy results on games which run to the first admissible in the play.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 2 , June 2006 , pp. 425 - 459
Copyright
Copyright © Association for Symbolic Logic 2006

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

[1]Jensen, R. Björn, The fine structure of the eonstructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972). pp. 229–308: erratum, ibid. 4 (1972), p. 443, With a section by Jack Silver.CrossRefGoogle Scholar
[2]Martin, Donald A., The largest countable this, that, and the other, Cabal Seminar '79–'81, Lecture Notes in Mathematics, vol. 1019, Springer, Berlin, 1983, pp. 97–106.CrossRefGoogle Scholar
[3]Martin, Donald A., A purely inductive proof of Borel determinacy, Recursion Theory (Ithaca, N. Y., 1982), Proceedings of the Symposium on Pure Mathematics, vol. 42. American Mathematical Society, Providence, RI, 1985. pp. 303–308.CrossRefGoogle Scholar
[4]Neeman, Itay, Unraveling Π11 sets, Annals of Pure and Applied Logic, vol. 106 (2000), no. 1–3, pp. 151–205.CrossRefGoogle Scholar
[5]Neeman, Itay, The determinacy of long games, de Gruyter Series in Logic and its Applications, vol. 7. Walter de Gruyter GmbH & Co., Berlin, 2004.CrossRefGoogle Scholar
[6]Neeman, Itay, Unraveling Π11 sets, revisited, Israel Journal of Mathematics, to appear.Google Scholar
[7]Steel, John R., Determinacy in the Mitchell models, Annals of Mathematical Logic, vol. 22 (1982), no. 2, pp. 109–125.CrossRefGoogle Scholar
[8]Steel, John R., Inner models with many Woodin cardinals, Annals of Pure and Applied Logic, vol. 65 (1993), no. 2, pp. 185–209.CrossRefGoogle Scholar
[9]Zeman, Martin, Inner models and large cardinals, de Gruyter Series in Logic and its Applications, vol. 5. Walter de Gruyter GmbH & Co., Berlin. 2002.CrossRefGoogle Scholar