Results 71 to 80 of about 199 (115)
Berkeley Cardinals and Vop\v{e}nka's Principle
We introduce "$n$-choiceless" supercompact and extendible cardinals in Zermelo-Fraenkel set theory without the Axiom of Choice. We prove relations between these cardinals and Vop\v{e}nka's Principle similar to those of Bagaria's work in his papers "$C ...
Mohammd, Marwan Salam
core
LARGE CARDINALS AND LIGHTFACE DEFINABLE WELL-ORDERS, WITHOUT THE GCH
, 2015 . This paper deals with the question whether the assumption that for every inaccessible cardinal κ there is a well-order of H(κ+) definable over the structure 〈H(κ+),∈ 〉 by a formula without parameters is consistent with the existence of (large) large ...
Philipp Lücke +2 more
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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
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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
Forcing “NS_{ω_1} is ω_1-dense” from large cardinals - a journey guided by the stars
The nonstationary ideal on ω_1 is ω_1-dense if there is a set B of ω_1-many stationary subsets of ω_1 that every stationary subset of ω_1 contains an element of S on a club.
Lietz, Andreas Theodor
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CONSECUTIVE SINGULAR CARDINALS AND THE CONTINUUM FUNCTION
, 2012 We show that from a supercompact cardinal κ, there is a forcing extension V [G] that has a symmetric inner model N in which ZF + ¬AC holds, κ and κ+ are both singular, and the continuum function at κ can be precisely controlled, in the sense that the ...
Arthur W. Apter, Brent Cody
core
On the super tree property and on large cardinals in HOD
This thesis is divided into two parts. The first part is a work on the super tree property, a strengthening of the tree property. From Specker's theorem, the continuum hypothesis must fail at $kappa$ if we want the tree property at $kappa ...
core +1 more source
Contributions to the Theory of Large Cardinals Beyond Choice
[eng] This thesis investigates large cardinals that are inconsistent with the Axiom of Choice. First, we characterize Berkeley cardinals in terms of a restricted form of Vopěnka’s Principle, and determine the consistency strength of several related ...
Mohammd, Marwan Salam
core +1 more source
Large infinities and definable sets. [PDF]
Proc Natl Acad Sci U S AAguilera JP, Bagaria J, Lücke P.
europepmc +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