Semi-proper forcing, remarkable cardinals, and Bounded Martin's Maximum

Mathematical Logic Quarterly 50 (6):527-532 (2004)
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Abstract

We show that L absoluteness for semi-proper forcings is equiconsistent with the existence of a remarkable cardinal, and hence by [6] with L absoluteness for proper forcings. By [7], L absoluteness for stationary set preserving forcings gives an inner model with a strong cardinal. By [3], the Bounded Semi-Proper Forcing Axiom is equiconsistent with the Bounded Proper Forcing Axiom , which in turn is equiconsistent with a reflecting cardinal. We show that Bounded Martin's Maximum is much stronger than BSPFA in that if BMM holds, then for every X ∈ V , X# exists

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Citations of this work

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References found in this work

1\ sets of reals.J. Bagaria & W. H. Woodin - 1997 - Journal of Symbolic Logic 62 (4):1379-1428.

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