相关论文: On the existence of large subsets of [lambda]^{<ka…

We show that the reduced cofinality of the nonstationary ideal NS_kappa on a regular uncountable cardinal kappa may be less than its cofinality, where the reduced cofinality of NS_kappa is the least cardinality of any family F of…

We prove that for lambda = beta_omega or just lambda strong limit singular of cofinality aleph_0, if there is a universal member in the class K^lf_lambda of locally finite groups of cardinality lambda, then there is a canonical one…

We call a pair of infinite cardinals $(\kappa,\lambda)$ with $\kappa > \lambda$ a dominating (resp. pinning down) pair for a topological space $X$ if for every subset $A$ of $X$ (resp. family $\mathcal{U}$ of non-empty open sets in $X$) of…

Recent results of Hindman, Leader and Strauss and of the second author and Rinot showed that some natural analogs of Hindman's Theorem fail for all uncountable cardinals. Results in the positive direction were obtained by Komj\'ath, the…

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 investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of indiscernibles over the universe. One of the main results of the paper shows that the purely set-theoretical…

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable…

We fully disprove a conjecture of Haythorpe on the minimum number of hamiltonian cycles in regular hamiltonian graphs, thereby extending a result of Zamfirescu, as well as correct and complement Haythorpe's computational enumerative results…

Let $\kappa$ be a regular limit cardinal, $\kappa \subseteq A$. We study a notion of $n$-s-stationarity on $\mathcal{P}_{\kappa}(A)$. We construct a sequence of topologies $\langle \tau_0, \tau_1, \dots \rangle $ on…

Given an uncountable cardinal $\kappa$, we consider the question of whether subsets of the power set of $\kappa$ that are usually constructed with the help of the Axiom of Choice are definable by $\Sigma_1$-formulas that only use the…

It is shown that every normalized weakly null sequence of length $\kappa_{\lambda}$ in a Banach space has a subsequence of length $\lambda$ which is an unconditional basic sequence; here $\kappa_{\lambda}$ is a large cardinal depending on a…

A study is carried out of the elementary theory of quotients of symmetric groups in a similar spirit to [Sh:24]. Apart from the trivial and alternating subgroups, the normal subgroups of the full symmetric group S(mu) on an infinite…

We give a necessary and sufficient condition for the following property of an integer $d\in\mathbb N$ and a pair $(a,A)\in\mathbb R^2$: There exist $\kappa > 0$ and $Q_0\in\mathbb N$ such that for all $\mathbf x\in \mathbb R^d$ and $Q\geq…

Let $\kappa$ be an infinite cardinal. A topological space $X$ is $\kappa$-bounded if the closure of any subset of cardinality $\le\kappa$ in $X$ is compact. We discuss the problem of embeddability of topological spaces into Hausdorff…

We present existence and nonexistence results on the solution of an overdetermined problem for the normalized p-Laplacian in a bounded open set, with p ranging from 1 to infinity. More precisely we consider a non-constant Neumann condition…

We develop Descriptive Set Theory in Generalized Baire Spaces without assuming $\kappa^{<\kappa}=\kappa$. We point out that without this assumption the basic topological concepts of these spaces have to be slightly modified in order to…

We prove that for infinite cardinals $\kappa<\lambda$ the alternating group $Alt(\lambda)$ (of even permutations) of $\lambda$ is not embeddable into the symmetric group $Sym(\kappa)$ (of all permutations) of $\kappa$. To prove this fact we…

We consider the two-cardinal Kurepa Hypothesis $\mathsf{KH}(\kappa,\lambda)$. We observe that if $\kappa\leq\lambda<\mu$ are infinite cardinals then…

Suppose $\kappa$ is a regular cardinal and $\bar a=\langle \mu_i: i<\kappa \rangle$ is a non-decreasing sequence of regular cardinals. We study the set of possible cofinalities of cuts Pcut$(\bar a)=\{(\lambda_1, \lambda_2):$ for some…

We try to build, provably in ZFC, for a first order T a model in which any isomorphism between two Boolean algebras is definable. The problem, compared to [Sh:384], is with pseudo-finite Boolean algebras. A side benefit is that we do not…