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ISSN 1088-6826(e) ISSN 0002-9939(p)

Diamonds

Author(s): Saharon Shelah
Journal: Proc. Amer. Math. Soc. 138 (2010), 2151-2161.
MSC (2010): Primary 03E04; Secondary 03E05, 03E35
Posted: 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 .

References:

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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: 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
Posted: 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
Copyright of article: Copyright 2010, American Mathematical Society

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