Parametrized ♢ principles

Moore, Justin; Hrušák, Michael; Džamonja, Mirna

doi:10.1090/S0002-9947-03-03446-9

Parametrized $\diamondsuit$ principles
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by Justin Tatch Moore, Michael Hrušák and Mirna Džamonja

Trans. Amer. Math. Soc. 356 (2004), 2281-2306

DOI: https://doi.org/10.1090/S0002-9947-03-03446-9

Published electronically: October 8, 2003

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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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