The Tree Property at ω₂ and Bounded Forcing Axioms
Sy-David Friedman; Víctor Torres-Pérez
Bulletin of the Polish Academy of Sciences. Mathematics (2015)
- Volume: 63, Issue: 3, page 207-216
- ISSN: 0239-7269
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topSy-David Friedman, and Víctor Torres-Pérez. "The Tree Property at ω₂ and Bounded Forcing Axioms." Bulletin of the Polish Academy of Sciences. Mathematics 63.3 (2015): 207-216. <http://eudml.org/doc/281143>.
@article{Sy2015,
abstract = {We prove that the Tree Property at ω₂ together with BPFA is equiconsistent with the existence of a weakly compact reflecting cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for ω₂ together with BPFA is equiconsistent with the existence of a reflecting Mahlo cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a Mahlo cardinal.},
author = {Sy-David Friedman, Víctor Torres-Pérez},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {tree property; bounded proper forcing axiom (BPFA); Aronszajn trees; special Aronszajn trees},
language = {eng},
number = {3},
pages = {207-216},
title = {The Tree Property at ω₂ and Bounded Forcing Axioms},
url = {http://eudml.org/doc/281143},
volume = {63},
year = {2015},
}
TY - JOUR
AU - Sy-David Friedman
AU - Víctor Torres-Pérez
TI - The Tree Property at ω₂ and Bounded Forcing Axioms
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2015
VL - 63
IS - 3
SP - 207
EP - 216
AB - We prove that the Tree Property at ω₂ together with BPFA is equiconsistent with the existence of a weakly compact reflecting cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for ω₂ together with BPFA is equiconsistent with the existence of a reflecting Mahlo cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a Mahlo cardinal.
LA - eng
KW - tree property; bounded proper forcing axiom (BPFA); Aronszajn trees; special Aronszajn trees
UR - http://eudml.org/doc/281143
ER -
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