Results 41 to 50 of about 218 (121)
, 2020 We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the axiom of choice this is equivalent to measurability, but it is well-known that choice is necessary for ...
Karagila, Asaf, Hayut, Yair
core +1 more source
Indestructible strong compactness but not supercompactness
, 2012 Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the least strongly compact and least supercompact cardinal and κ’s strong compactness, but not its supercompactness, is indestructible under arbitrary κ-directed ...
Sargsyan, Grigor +2 more
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Small embeddings, forcing with side conditions, and large cardinal characterizations [PDF]
, 2019 In this thesis, we provide new characterizations for several well-studied large cardinal notions. These characterizations will be of two types. Motivated by seminal work of Magidor, the first type characterizes large cardinals through the existence of so-
Njegomir, Ana
core
CHANG’S CONJECTURE, GENERIC ELEMENTARY EMBEDDINGS AND INNER MODELS FOR HUGE CARDINALS [PDF]
, 2015 We introduce a natural principle Strong Chang Reflection strengthening the classical Chang Conjectures. This principle is between a huge and a two huge cardinal in consistency strength.
FOREMAN, MATTHEW
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Global Chang's Conjecture and singular cardinals. [PDF]
Eur J Math, 2021 Eskew M, Hayut Y.
europepmc +1 more source
Stationary Reflection and the failure of SCH
, 2023 In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal $\nu$ such that the singular cardinal hypothesis fails at $\nu$ and every collection of fewer than $\mathrm{cf}(\nu)$ stationary subsets of $\
Unger, Spencer +2 more
core
Chang's conjecture may fail at supercompact cardinals
, 2006 We prove a revised version of Laver's indestructibility theorem which slightly improves over the classical result. An application yields the consistency of $(\kappa^+,\kappa)\notcc(\aleph_1,\aleph_0)$ when $\kappa$ is supercompact. The actual proofs show
Koenig, Bernhard
core
On Löwenheim-Skolem-Tarski numbers for extensions of first order logic
, 2011 We show that, assuming the consistency of a supercompact cardinal, the first (weakly) inaccessible cardinal can satisfy a strong form of a Löwenheim-Skolem-Tarski theorem for the equicardinality logic L(I), a logic introduced in [5] strictly between ...
Väänänen, J. +3 more
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THE LEAST WEAKLY COMPACT CARDINAL CAN BE UNFOLDABLE, WEAKLY MEASURABLE AND NEARLY θ-SUPERCOMPACT
, 2013 We provefrom suitable largecardinalhypothesesthat the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly θ-supercompact, for any desired θ.
Moti Gitik +3 more
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FORCING AXIOMS, SUPERCOMPACT CARDINALS, SINGULAR CARDINAL COMBINATORICS
, 2007 The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals.
Matteo Viale, Viale, Matteo
core