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Parametrized principles
Authors:Justin Tatch Moore  Michael Hrusá  k  Mirna Dzamonja
Institution:Department of Mathematics, Boise State University, Boise, Idaho 83725 ; Institute of Mathematics, University Nacional Autonoma de Mexico, Apartado Postal 27-3, 58089 Morelia, Mexico ; School of Mathematics, University of East Anglia, Norwich, England NR4 7TJ
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.

Keywords:Diamond  weak diamond  cardinal invariant  guessing principle
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