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Parametrized $\diamondsuit$ principles

Authors: Justin Tatch Moore, Michael Hrusák and Mirna Dzamonja
Journal: Trans. Amer. Math. Soc. 356 (2004), 2281-2306
MSC (2000): Primary 03E17, 03E65
Published electronically: October 8, 2003
MathSciNet review: 2048518
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Abstract: 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

Michael Hrusák
Affiliation: Institute of Mathematics, University Nacional Autonoma de Mexico, Apartado Postal 27-3, 58089 Morelia, Mexico

Mirna Dzamonja
Affiliation: School of Mathematics, University of East Anglia, Norwich, England NR4 7TJ

Keywords: Diamond, weak diamond, cardinal invariant, guessing principle
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.
Article copyright: © Copyright 2003 American Mathematical Society