科研之友
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摘要
If the bounded proper forcing axiom BPFA holds and omega(1) = omega(L)(1), then there is a lightface Sigma(1)(3) well-ordering of the reals. The argument combines a well-ordering due to Caicedo-Velickovic 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 Sigma(1)(4), for many "consistently locally certified" relations R on R. This is accomplished through a use of David's trick and a coding through the Sigma(2) stable ordinals of L.
- 出版日期2011-12
