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Can a large cardinal be forced from a condition implying its negation?
Author(s):
Arthur
W.
Apter;
Grigor
Sargsyan
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3103-3108.
MSC (2000):
Primary 03E02, 03E35, 03E55
Posted:
May 4, 2005
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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.
References:
-
- 1.
- A. Apter, J. D. Hamkins, ``Exactly Controlling the Non-Supercompact Strongly Compact Cardinals'', Journal of Symbolic Logic 68, 2003, 669-688. MR 1976597 (2004b:03075)
- 2.
- A. Apter, J. Henle, ``Relative Consistency Results via Strong Compactness'', Fundamenta Mathematicae 139, 1991, 133-149. MR 1150596 (93h:03071)
- 3.
- K. Devlin, ``Some Weak Versions of Large Cardinal Axioms'', Annals of Mathematical Logic 5, 1973, 291-325.MR 0363906 (51:161)
- 4.
- J. Henle, ``Partition Properties and Prikry Forcing'', Journal of Symbolic Logic 55, 1990, 938-947.MR 1071307 (91k:03132)
- 5.
- A. Kanamori, The Higher Infinite, Springer-Verlag Publishing Company, Berlin and New York, 1994. MR 1321144 (96k:03125)
- 6.
- E. Kleinberg, ``Rowbottom Cardinals and Jonsson Cardinals are Almost the Same'', Journal of Symbolic Logic 38, 1973, 423-427. MR 0337616 (49:2385)
- 7.
- E. Kleinberg, ``The Equiconsistency of Two Large Cardinal Axioms'', Fundamenta Mathematicae 102, 1979, 81-85. MR 0525930 (80d:03056)
- 8.
- P. Larson, The Stationary Tower, University Lecture Series, vol. 32, American Mathematical Society, Providence, RI, 2004. MR 2069032
- 9.
- A. Lévy, R. Solovay, ``Measurable Cardinals and the Continuum Hypothesis'', Israel Journal of Mathematics 5, 1967, 234-248.MR 0224458 (37:57)
- 10.
- S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Clarendon Press, Oxford, 1994.MR 1318912 (96e:03001)
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Additional Information:
Arthur
W.
Apter
Affiliation:
Department of Mathematics, Baruch College of CUNY, New York, New York 10010
Email:
awabb@cunyvm.cuny.edu
Grigor
Sargsyan
Affiliation:
Group in Logic and the Methodology of Science, University of California, Berkeley, California 94720
Email:
grigor@math.berkeley.edu
DOI:
10.1090/S0002-9939-05-07840-8
PII:
S 0002-9939(05)07840-8
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
Posted:
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.
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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