Paper Info
Title
Bounded forcing axioms as principles of generic absoluteness
Abstract
.   We show that Bounded Forcing Axioms (for instance, Martin's Axiom, the Bounded Proper Forcing Axiom, or the Bounded Martin's Maximum) are equivalent to principles of generic absoluteness, that is, they assert that if a sentence of the language of set theory with parameters of small transitive size is forceable, then it is true. We also show that Bounded Forcing Axioms imply a strong form of generic absoluteness for projective sentences, namely, if a sentence with parameters is forceable, then it is true. Further, if for every real x, exists, and the second uniform indiscernible is less than , then the same holds for sentences.
Year
DOI
Venue
2000
10.1007/s001530050154
Arch. Math. Log.
Keywords
Field
DocType
set theory
Discrete mathematics,Set theory,Combinatorics,Absoluteness,Axiom,Forcing (mathematics),Proper forcing axiom,Sentence,Mathematics,Transitive relation,Bounded function
Journal
Volume
Issue
ISSN
39
6
0933-5846
Citations 
PageRank 
References 
20
2.38
3
Authors
1
Name
Order
Citations
PageRank
Joan Bagaria16313.15