BPFA and Projective Well-Orderings of the Reals

Authors

Andrés Eduardo Caicedo, Boise State UniversityFollow
Sy-David Friedman, University of Vienna

Document Type

Article

Publication Date

12-1-2011

Abstract

If the bounded proper forcing axiom BPFA holds and ω₁=ω₁^L, then there is a lightface Σ¹₃ well-ordering of the reals. The argument combines a well-ordering due to Caicedo-Veličković with an absoluteness result for models of MA in the spirit of "David's trick." We also present a general coding scheme that allows us to show that BPFA is equiconsistent with R being lightface Σ¹₄, for many "consistently locally certified" relations R on ℝ. This is accomplished through a use of David's trick and a coding through the Σ₂ stable ordinals of L.

Publication Information

Caicedo, Andrés Eduardo and Friedman, Sy-David. (2011). "BPFA and Projective Well-Orderings of the Reals". Journal of Symbolic Logic, 76(4), 1126-1136. https://doi.org/10.2178/jsl/1318338842