It is proved that if an uncountable cardinal κ has ineffable subset of weakly compact cardinals, then a cardinal, and Ramsey (Rowbottom, Jónsson, or subtle) J\'onsson, cardinal.

We use Shelah’s theory of possible cofinalities in order to solve some problems about ultrafilters. Theorem 1. Suppose that λ is a singular cardinal, λ′ < λ, and the ultrafilter D is κ-decomposable for all regular cardinals κ with λ′ < κ < λ. Then D is either λ-decomposable, or λ-decomposable. Corollary 2. If λ is a singular cardinal, then an ultrafilter is (λ, λ)-regular if and only if it is e...

In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

Let μ be singular of uncountable cofinality. If μ > 2cf(μ), we prove that in P = ([μ],⊇) as a forcing notion we have a natural complete embedding of Levy(א0, μ+) (so P collapses μ+ to א0) and even Levy(א0,UJbd κ (μ)). The “natural” means that the forcing ({p ∈ [μ] : p closed},⊇) is naturally embedded and is equivalent to the Levy algebra. Moreover we prove more than conjectured: if P fails the ...

We construct a model in which for all 1 ≤ n < ω, there is no stationary subset of אn+1 ∩ cof(אn) which carries a partial square. Let κ be an uncountable cardinal and let μ ≤ κ be regular. A set A ⊆ κ∩cof(μ) is said to carry a partial square if there exists a sequence ⟨cα : α ∈ A⟩ such that each cα is club in α with order type μ, and for all γ which is a common limit point of cα and cβ , cα ∩ γ ...

We show that if M is a stable unsuperstable homogeneous structure, then for most κ < |M| , the number of elementary submodels of M of power κ is 2 . Through out this paper we assume that M is a stable unsuperstable homogeneous model such that |M| is strongly inaccessible (= regular and strong limit). We can drop this last assumption if instead of all elementary submodels of M we study only suit...

The ring loading problem with integer demand splitting is that of routing κ traffic requirements on an undirected ring network. We present a compact polyhedral description of the set of feasible solutions to the problem, whose number of variables and constraints is O(κ). © 2009 Elsevier B.V. All rights reserved.

Abstract In dimensions n ≥ 4 {n\geq 4} , an ancient κ-solution is a nonflat, complete, solution of the Ricci flow that uniformly PIC and weakly PIC2; has bounded curvature; κ-noncollapsed. this paper, we study classification κ-solutions to n -dimensional on S<...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...