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Can a large cardinal be forced from a condition implying its negation?

Authors: Arthur W. Apter and Grigor Sargsyan
Journal: Proc. Amer. Math. Soc. 133 (2005), 3103-3108
MSC (2000): Primary 03E02, 03E35, 03E55
Published electronically: May 4, 2005
MathSciNet review: 2159791
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we provide an affirmative answer to the title question by giving two examples of cardinals satisfying conditions implying they are non-Rowbottom which can be turned into Rowbottom cardinals via forcing. In our second example, our cardinal is also non-Jonsson.

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Additional Information

Arthur W. Apter
Affiliation: Department of Mathematics, Baruch College of CUNY, New York, New York 10010

Grigor Sargsyan
Affiliation: Group in Logic and the Methodology of Science, University of California, Berkeley, California 94720

Keywords: Jonsson cardinal, Rowbottom cardinal, strongly compact cardinal
Received by editor(s): August 30, 2003
Received by editor(s) in revised form: February 14, 2004, and June 15, 2004
Published electronically: May 4, 2005
Additional Notes: Both authors wish to thank the CUNY Research Foundation for having provided partial support for this research via the first author’s PSC-CUNY Grant 64455-00-33, under which the second author was a research assistant. In addition, we wish to thank the referee and Carl Jockusch, the communicating editor, for helpful comments, corrections, and suggestions which have been incorporated into this version of the paper and which have considerably improved the presentation of the material contained herein.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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