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Forcing axioms, well orderings of the reals, and inner models of set theory
by
Boban Velickovic
Universite de Paris 7
Coauthors: Andres Caicedo, California Institute of Technology
We consider to what extent is the model of a strong forcing axiom such as PFA, MM, or one of their fragments determined by its cardinals. The general question is the following: given two models of say PFA, V and W, which have the same cardinals, do V and W have the same w1 sequences of ordinals?
We present some recent results and discuss directions for future work. In particular, we show that BPFA implies the existence of a D1 well ordering of the reals and we discuss Viale's recent proof that PFA implies the Singular Cardinal Hypothesis.
The key technical tools we use are Moore's Mapping Reflection Principle and the P-ideal dichotomy.
Date received: March 19, 2006
Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # casb-12.