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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Parametrized $\diamondsuit$ principles
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by Justin Tatch Moore, Michael Hrušák and Mirna Džamonja PDF
Trans. Amer. Math. Soc. 356 (2004), 2281-2306 Request permission


We will present a collection of guessing principles which have a similar relationship to $\diamondsuit$ as cardinal invariants of the continuum have to CH. The purpose is to provide a means for systematically analyzing $\diamondsuit$ and its consequences. It also provides for a unified approach for understanding the status of a number of consequences of CH and $\diamondsuit$ in models such as those of Laver, Miller, and Sacks.
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Additional Information
  • Justin Tatch Moore
  • Affiliation: Department of Mathematics, Boise State University, Boise, Idaho 83725
  • MR Author ID: 602643
  • Email:
  • Michael Hrušák
  • Affiliation: Institute of Mathematics, University Nacional Autonoma de Mexico, Apartado Postal 27-3, 58089 Morelia, Mexico
  • MR Author ID: 602083
  • ORCID: 0000-0002-1692-2216
  • Email:
  • Mirna Džamonja
  • Affiliation: School of Mathematics, University of East Anglia, Norwich, England NR4 7TJ
  • ORCID: setImmediate$0.3709267400444315$1
  • Email:
  • Received by editor(s): September 12, 2002
  • Published electronically: October 8, 2003
  • Additional Notes: The first and third authors received support from EPSRC grant GR/M71121 for the research of this paper. The research of the second author was supported in part by the Netherlands Organization for Scientific Research (NWO) – Grant 613.007.039, and in part by the Grant Agency of the Czech Republic – Grant GAČR 201/00/1466.
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 2281-2306
  • MSC (2000): Primary 03E17, 03E65
  • DOI:
  • MathSciNet review: 2048518