Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-07-26T03:23:53.869Z Has data issue: false hasContentIssue false
  • English
  • Français

Counterexamples to the unique and cofinal branches hypotheses

Published online by Cambridge University Press:  12 March 2014

Itay Neeman  and
John Steel
Itay Neeman
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095-1555, USA.E-mail:ineeman@math.ucla.edu
John Steel
Affiliation:
Department of Mathematics, University of California Berkeley, Berkeley, CA 94720-3840, USA.E-mail:steel@math.berkeley.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We produce counterexamples to the unique and cofinal branches hypotheses, assuming (slightly less than) the existence of a cardinal which is strong past a Woodin cardinal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 3 , September 2006 , pp. 977 - 988
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]Andretta, Alessandro, Large cardinals and iteration trees of height ω, Annals of Pure and Applied Logic, vol. 54 (1991), no. 1, pp. 1–15.CrossRefGoogle Scholar
[2]Martin, Donald A. and Steel, John R., A proof of projective determinacy, Journal of the American Mathematical Society, vol. 2 (1989), no. 1, pp. 71–125.CrossRefGoogle Scholar
[3]Martin, Donald A. and Steel, John R., Iteration trees, Journal of the American Mathematical Society, vol. 7 (1994), no. 1, pp. 1–73.CrossRefGoogle Scholar
[4]Neeman, Itay, Inner models in the region of a Woodin limit of Woodin cardinals, Annals of Pure and Applied Logic, vol. 116 (2002), no. 1–3, pp. 67–155.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., KG, Berlin, 2004.CrossRefGoogle Scholar
[6]Steel, John R., Core models with more Woodin cardinals, this Journal, vol. 67 (2002), no. 3, pp. 1197–1226.Google Scholar
[7]Steel, John R., Local Kc -constructions, to appear.Google Scholar