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PFA and guessing models
- Source :
- Israel Journal of Mathematics. 215:607-667
- Publication Year :
- 2016
- Publisher :
- Springer Science and Business Media LLC, 2016.
-
Abstract
- This paper explores the consistency strength of The Proper Forcing Axiom ($\textsf{PFA}$) and the theory (T) which involves a variation of the Viale-Wei$\ss$ guessing hull principle. We show that (T) is consistent relative to a supercompact cardinal. The main result of the paper implies that the theory "$\sf{AD}$$_\mathbb{R} + \Theta$ is regular" is consistent relative to (T) and to $\textsf{PFA}$. This improves significantly the previous known best lower-bound for consistency strength for (T) and $\textsf{PFA}$, which is roughly "$\sf{AD}$$_\mathbb{R} + \textsf{DC}$".
- Subjects :
- Pure mathematics
General Mathematics
010102 general mathematics
Supercompact cardinal
03E45, 03E55, 03E47
Mathematics::General Topology
Mathematics - Logic
01 natural sciences
Mathematics::Logic
Variation (linguistics)
Consistency (statistics)
Hull
0103 physical sciences
FOS: Mathematics
Proper forcing axiom
010307 mathematical physics
0101 mathematics
Algebra over a field
Logic (math.LO)
Mathematics
Subjects
Details
- ISSN :
- 15658511 and 00212172
- Volume :
- 215
- Database :
- OpenAIRE
- Journal :
- Israel Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....7679cfae66aefe5088bc46f8f77f0fcc