Parametrized diamond principles I.
by
Michael Hrusak
UNAM, Mexico
Coauthors: M. Dzamonja (University of East Anglia), J. T. Moore (Boise State University)

We introduce a collection of guessing principles, which relate to Jensen's diamond principle in a similar way as cardinal invariants of the continuum relate to the continuum hypothesis. We show that these guessing principles often hold in standard forcing extensions. Classical diamond constructions are recast into this framework, reducing the hypotheses necessary for the construction to be carried out. The impact of these principles on the cardinal invariants of the continuum will also be mentioned.

Date received: February 21, 2002