Results 71 to 80 of about 218 (121)
The determination of the exact consistency strength of the Proper Forcing Axiom (PFA) and its strengthening, Martin's Maximum (MM), remains one of the central open problems in modern set theory. While the consistency of these axioms was established relative to a supercompact cardinal by Baumgartner and Foreman-Magidor-Shelah respectively, the question ...
Revista, Zen, MFC, 10
openaire +1 more source
A note on strong compactness and resurrectibility
, 2000 We construct a model containing a proper class of strongly compact cardinals in which no strongly compact cardinal κ is κ+ supercompact and in which every strongly compact cardinal has its strong compactness ...
Arthur W. Apter, Apter, Arthur
core
The determination of the exact consistency strength of the Proper Forcing Axiom (PFA) remains one of the central open problems in modern set theory. While the consistency of PFA was established by Baumgartner relative to a supercompact cardinal, recent developments in inner model theory and forcing iterations have significantly narrowed the gap between
Revista, Zen, MFC, 10
openaire +2 more sources
PFA and the Definability of the Nonstationary Ideal
We produce, relative to a ZFC model with a supercompact cardinal, a ZFC model of the Proper Forcing Axiom in which the nonstationary ideal on ω1 is ∏1-definable in a parameter from ...
Larson, Paul; orcid: +3 more
core +1 more source
Partition properties of subsets of Pκλ
, 1999 Let κ > ω be a regular cardinal and λ > κ a cardinal. The following partition property is shown to be consistent relative to a supercompact cardinal: For any $f : ∪_{n < ω}[X]^{n}_⊂ → γ$ with $X⊂P_κλ$ unbounded and 1 < γ < κ there is an unbounded Y ∪ X ...
Shioya, Masahiro
core
Inner Model Theory for Supercompact Cardinals and the Consistency of the Proper Forcing Axiom
Mathematical Applications of Science Fiction We construct a canonical inner model L[E] for a super-compact cardinal, extending the hyper-Woodin hierarchythrough a fully iterable extender sequence E allowing forlong extenders. We establish the existence of a comparisonprocess for mice exhibiting λ-supercompactness, resolvingthe iterability problem ...
Revista, Zen, MFC, 10
openaire +2 more sources
Large infinities and definable sets. [PDF]
Proc Natl Acad Sci U S AAguilera JP, Bagaria J, Lücke P.
europepmc +1 more source
Some variations on the partition property for normal ultrafilters on Pkl
, 1993 Suppose κ is a supercompact cardinal and λ≥κ. In [3], we studied the relationship between the weak partition property and the partition property for normal ultrafilters on $P_κλ$.
Barbanel, Julius
core