Diamonds
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- by Saharon Shelah PDF
- Proc. Amer. Math. Soc. 138 (2010), 2151-2161 Request permission
Abstract:
If $\lambda = \chi ^+ = 2^\chi > \aleph _1$, then diamond on $\lambda$ holds. Moreover, if $\lambda = \chi ^+ = 2^\chi$ and $S \subseteq \{\delta < \lambda :\text {cf}(\delta ) \ne \text {cf}(\chi )\}$ is stationary, then $\diamondsuit _S$ holds. Earlier this was known only under additional assumptions on $\chi$ and/or $S$.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
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il
- 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
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 2151-2161
- MSC (2010): Primary 03E04; Secondary 03E05, 03E35
- DOI: https://doi.org/10.1090/S0002-9939-10-10254-8
- MathSciNet review: 2596054