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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Diamonds


Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 138 (2010), 2151-2161
MSC (2010): Primary 03E04; Secondary 03E05, 03E35
Published electronically: February 12, 2010
MathSciNet review: 2596054
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Abstract: If $ \lambda = \chi^+ = 2^\chi > \aleph_1$, then diamond on $ \lambda$ holds. Moreover, if $ \lambda = \chi^+ = 2^\chi$ and $ S \subseteq \{\delta < \lambda:$cf$ (\delta) \ne$   cf$ (\chi)\}$ is stationary, then $ \diamondsuit_S$ holds. Earlier this was known only under additional assumptions on $ \chi$ and/or $ S$.


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Additional Information

Saharon Shelah
Affiliation: Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel – and – Department of Mathematics, Hill Center - Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Email: shelah@math.huji.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10254-8
PII: S 0002-9939(10)10254-8
Received by editor(s): March 24, 2008
Received by editor(s) in revised form: July 7, 2008, February 26, 2009, and October 15, 2009
Published electronically: February 12, 2010
Additional Notes: This research was supported by the United-States-Israel Binational Science Foundation (Grant No. 2002323), Publication No. 922. The author thanks Alice Leonhardt for the beautiful typing.
Communicated by: Julia Knight
Article copyright: © Copyright 2010 American Mathematical Society