Kappa-Slender Modules
For an arbitrary infinite cardinal , we define classes of -cslender and -tslender modules as well as related classes of -hmodules and initiate a study of these classes.
Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH
Starting from large cardinals we construct a pair V₁⊆ V₂ of models of ZFC with the same cardinals and cofinalities such that GCH holds in V₁ and fails everywhere in V₂.
Klassen von Moduln über Dedekind-Ringen und Satz von Stein-Serre
Kleinberg sequences and partition cardinals below δ₅¹
The author computes the Kleinberg sequences derived from the three different normal ultrafilters on δ₃¹.
Kurepa's Hypothesis and a Problem of Ulam on Families of Measures.
Kurepa's hypothesis and the continuum
Large cardinals and covering numbers
The paper is concerned with the computation of covering numbers in the presence of large cardinals. In particular, we revisit Solovay's result that the Singular Cardinal Hypothesis holds above a strongly compact cardinal.
Large cardinals and Dowker products
We prove that if there is a model of set-theory which contains no first countable, locally compact, scattered, countably paracompact space , whose Tychonoff square is a Dowker space, then there is an inner model which contains a measurable cardinal.
Le problème des cardinaux singuliers
Left-distributive embedding algebras.
Level by level equivalence and the number of normal measures over
We construct two models for the level by level equivalence between strong compactness and supercompactness in which if κ is λ supercompact and λ ≥ κ is regular, we are able to determine exactly the number of normal measures carries. In the first of these models, carries many normal measures, the maximal number. In the second of these models, carries many normal measures, except if κ is a measurable cardinal which is not a limit of measurable cardinals. In this case, κ (and hence also )...
Level by Level Inequivalence, Strong Compactness, and GCH
We construct three models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In the first two models, below the supercompact cardinal κ, there is a non-supercompact strongly compact cardinal. In the last model, any suitably defined ground model Easton function is realized.
Linear orders and MA + ¬wKH
I prove that the statement that “every linear order of size can be embedded in ” is consistent with MA + ¬ wKH.
L-like Combinatorial Principles and Level by Level Equivalence
We force and construct a model in which GCH and level by level equivalence between strong compactness and supercompactness hold, along with certain additional “L-like” combinatorial principles. In particular, this model satisfies the following properties: (1) holds for every successor and Mahlo cardinal δ. (2) There is a stationary subset S of the least supercompact cardinal κ₀ such that for every δ ∈ S, holds and δ carries a gap 1 morass. (3) A weak version of holds for every infinite cardinal...
Locally compact perfectly normal spaces may all be paracompact
We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...
L'ordre de Dehornoy sur les tresses
Making the hugeness of ϰ resurrectable after ϰ-directed closed forcing
Maximal σ-independent families
Measurable cardinals and analytic games
Measurable cardinals and category bases
We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.