Results 61 to 70 of about 199 (115)
Homogeneous changes in cofinalities with applications to HOD
, 2017 We present a new technique for changing the cofinality of large cardinals using homogeneous forcing. As an application we show that many singular cardinals in [Formula: see text] can be measurable in HOD.
Omer Ben-Neria, Spencer Unger
core +1 more source
Definable orthogonality classes in accessible categories are small
, 2013 International audienceWe lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopěnka's principle. We prove that the necessary large-cardinal
Rosický, Jirí +3 more
core +1 more source
Calculus on Strong Partition Cardinals
, 2006 In [HM] it was shown that if κ is a strong partition cardinal then every function from [κ] κ to [κ] κ is continuous almost everywhere. In this investigation, we explore whether such functions are differentiable or integrable in any sense.
J. M. Henle
core
Laver Sequences for Extendible and Super-Almost-Huge Cardinals
, 1997 Versions of Laver sequences are known to exist for supercompact and strong cardinals. Assuming very strong axioms of infinity, Laver sequences can be constructed for virtually any globally defined large cardinal not weaker than a strong cardinal; indeed,
Paul Corazza
core
The Proper Forcing Axiom (PFA) represents a significant strengthening of Martin's Axiom, asserting the existence of generic filters for a broad class of proper partial orders. This monograph investigates the consistency strength of PFA, situating it within the hierarchy of large cardinals.
Revista, Zen, MFC, 10
openaire +2 more sources
Forcing "$\mathrm{NS}_{\omega_1}$ is $\omega_1$-dense" From Large Cardinals
We answer a question of Woodin by showing that assuming an inaccessible cardinal $\kappa$ which is a limit of ${
Lietz, Andreas
core
, 2019 The inner model problem for supercompact cardinals, one of the central open problems in modern set theory, asks whether there is a canonical model of set theory with a supercompact cardinal.
Goldberg, Gabriel
core
On the consistency strength of the proper forcing axiom
, 2011 In recent work, the second author extended combinatorial principles due to Jech and Magidor that characterize certain large cardinal properties so that they can also hold true for small cardinals.
Christoph Weiß +3 more
core +1 more source
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