Cofinality changes required for a large set of unapproachable ordinals below

Author:
M. C. Stanley

Journal:
Proc. Amer. Math. Soc. **135** (2007), 2619-2622

MSC (2000):
Primary 03E05

Published electronically:
February 28, 2007

MathSciNet review:
2302583

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Abstract | References | Similar Articles | Additional Information

Abstract: In , assume that is a strong limit cardinal and . Let be the set of approachable ordinals less than . An open question of M. Foreman is whether can be non-stationary in some and preserving extension of . It is shown here that if is such an outer model, then is infinite, for each positive integer .

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Additional Information

**M. C. Stanley**

Affiliation:
Mathematics Department, San Jose State University, San Jose, California 95192

Email:
stanley@math.sjsu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-08760-6

Keywords:
Approachable ordinal,
$I[\lambda ]$,
cofinality,
Erd\H os-Rado

Received by editor(s):
December 6, 2005

Received by editor(s) in revised form:
April 19, 2006, and April 28, 2006

Published electronically:
February 28, 2007

Additional Notes:
Research supported by NSF grant DMS-0501114

Communicated by:
Julia Knight

Article copyright:
© Copyright 2007
American Mathematical Society