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December 2011 BPFA and projective well-orderings of the reals
Andrés Eduardo Caicedo, Sy-David Friedman
J. Symbolic Logic 76(4): 1126-1136 (December 2011). DOI: 10.2178/jsl/1318338842

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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Andrés Eduardo Caicedo. Sy-David Friedman. "BPFA and projective well-orderings of the reals." J. Symbolic Logic 76 (4) 1126 - 1136, December 2011. https://doi.org/10.2178/jsl/1318338842

Information

Published: December 2011
First available in Project Euclid: 11 October 2011

zbMATH: 1252.03107
MathSciNet: MR2895389
Digital Object Identifier: 10.2178/jsl/1318338842

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 4 • December 2011
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