### BPFA and projective well-orderings of the reals

Andrés Eduardo Caicedo and Sy-David Friedman
Source: J. Symbolic Logic Volume 76, Issue 4 (2011), 1126-1136.

#### Abstract

If the bounded proper forcing axiom BPFA holds and ω11L, 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.

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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1318338842
Digital Object Identifier: doi:10.2178/jsl/1318338842
Zentralblatt MATH identifier: 05991451
Mathematical Reviews number (MathSciNet): MR2895389

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