相关论文: A partition relation using strongly compact cardin…

A space X is kappa-resolvable (resp. almost kappa-resolvable) if it contains kappa dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets of X). Answering a problem raised by Juhasz, Soukup, and…

We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma_1$-definability at uncountable regular cardinals. In particular we give its exact consistency strength firstly in terms of the second…

The relations M(kappa,lambda,mu)->B [resp. B(sigma)] meaning that if A subset [kappa]^lambda with |A|=kappa is mu-almost disjoint then A has property B [resp. has a sigma-transversal] had been introduced and studied under GCH by Erdos and…

In the context of large cardinals, the classical diamond principle Diamond_kappa is easily strengthened in natural ways. When kappa is a measurable cardinal, for example, one might ask that a Diamond_kappa sequence anticipate every subset…

We present a version with non-definable forcing notions of Shelah's theory of iterated forcing along a template. Our main result, as an application, is that, if $\kappa$ is a measurable cardinal and $\theta<\kappa<\mu<\lambda$ are…

A simple \(P_\lambda\)-point on a regular cardinal \(\kappa\) is a uniform ultrafilter on \(\kappa\) with a mod-bounded decreasing generating sequence of length \(\lambda\). We prove that if there is a simple $P_\lambda$-point ultrafilter…

We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be virtually arbitrary. Specifically, we prove if V is a model…

From large cardinals we show the consistency of normal, fine, $\kappa$-complete $\lambda$-dense ideals on $\mathcal{P}_\kappa(\lambda)$ for successor $\kappa$. We explore the interplay between dense ideals, cardinal arithmetic, and squares,…

We introduce the family of axioms, denoted $\operatorname{Slice}_\kappa$, that claim the existence of strictly increasing decompositions of the form $$2^{\delta}=\bigcup_{\alpha<\kappa} 2^{\delta}\cap M_\alpha,$$ where $\delta<\kappa$, and…

We address a number of problems on Boolean Algebras. For example, we construct, in ZFC, for any BA B, and cardinal kappa BAs B_1,B_2 extending B such that the depth of the free product of B_1,B_2 over B is strictly larger than the depths of…

We establish the asymptotic regularity and the $\Delta$-convergence of the sequence constructed by the alternating projections to closed convex sets in a CAT($\kappa$) space with $\kappa > 0$. Furthermore, the strong convergence of the…

We investigate the extent to which ultrapowers by normal measures on $\kappa$ can be correct about powersets $\mathcal{P}(\lambda)$ for $\lambda>\kappa$. We consider two versions of this questions, the capturing property…

Working in the context of restricted forms of the Axiom of Choice, we consider the problem of splitting the ordinals below $\lambda$ of cofinality $\theta$ into $\lambda$ many stationary sets, where $\theta < \lambda$ are regular cardinals.…

We prove from suitable large cardinal hypotheses that the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly $\theta$-supercompact, for any desired $\theta$. In addition, we prove several global results…

Assuming an inaccessible cardinal kappa, there is a generic extension in which MA + 2^{aleph_0} = kappa holds and the reals have a Delta^2_1 well-ordering.

We discuss the existence of complete accumulation points of sequences in products of topological spaces. Then we collect and generalize many of the results proved in Parts I, II and IV. The present Part VI is complementary to Part V to the…

The main result of this paper is to show that for any compact space $X$ and any family $\{f_\alpha \colon \alpha< 2^\kappa, f_\alpha \colon X \stackrel{onto}{\longrightarrow} \beta \kappa\}$ of open mappings there exists a point $x \in X$…

In this paper, we prove that if $\kappa$ is a almost strongly compact cardinal, then any MAEC with L\"owenheim-Skolem number below $\kappa$ is $<\kappa$-d-tame.

Assuming 0^sharp does not exist, kappa is an uncountable cardinal and for all cardinals lambda with kappa <= lambda < kappa^{+ omega}, 2^lambda = lambda^+, we present a ``mini-coding'' between kappa and kappa^{+ omega}. This allows us to…

In a recent preprint, Garti and Shelah state that the techniques of a paper of Dzamonja and Shelah can be used to force u_kappa to be kappa^+ for supercompact kappa with 2^kappa arbitrarily large. In this expository article we spell out the…