The following pcf results are proved: 1. Assume that κ > א0 is a weakly compact cardinal. Let μ > 2κ be a singular cardinal of cofinality κ. Then for every regular λ < pp+Γ(κ)(μ) there is an increasing sequence ⟨λi | i < κ⟩ of regular cardinals converging to μ such that λ = tcf( ∏ i<κ λi, <Jbd κ ). 2. Let μ be a strong limit cardinal and θ a cardinal above μ. Suppose that at least one of them h...

The weakly compact reflection principle Reflwcpκq states that κ is a weakly compact cardinal and every weakly compact subset of κ has a weakly compact proper initial segment. The weakly compact reflection principle at κ implies that κ is an ω-weakly compact cardinal. In this article we show that the weakly compact reflection principle does not imply that κ is pω ` 1qweakly compact. Moreover, we...

It is shown that if κ > 2א0 and κ is less than the first inaccessible cardinal then every automorphism of P(κ)/[κ]<א0 is trivial outside of a set of cardinality 2א0 .

We show that for any infinite cardinal κ, every (κ+1)-strategically closed poset is κ+-strategically closed if and only if κ holds. This extends previous results of Velleman, et.al.

Lemma 1. For any > 0 and κ ∈ [, 1], we have V(κ) − V(κ −) ≤ Cα log 2 (1//). Proof. By monotonicity, it suffices to prove that result for κ = 1. Notice that for K ≥ 2α,

structures Jia-Liang Le, Zdeněk P. Bažant, and Martin Z. Bazant Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA Department of Materials Science, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA Department of Chemical Engineering and Department of Mathematics, Massachusetts Institute of Techno...

Mediate Disparate Responses to β B κ and I α B κ B Inhibitory Proteins I κ The NF

We investigate the problem if every compact space K carrying a Radon measure of Maharam type κ can be continuously mapped onto the Tikhonov cube [0, 1] (κ being an uncountable cardinal). We show that for κ ≥ cf(κ) ≥ ω2 this holds if and only if κ is a precaliber of measure algebras. Assuming that there is a family of ω1 null sets in 21 such that every perfect set meets one of them, we construct...

We study various classes of maximality principles, MP(κ,Γ), introduced by J.D. Hamkins in [6], where Γ defines a class of forcing posets and κ is an infinite cardinal. We explore the consistency strength and the relationship of MP(κ,Γ) with various forcing axioms when κ ∈ {ω, ω1}. In particular, we give a characterization of bounded forcing axioms for a class of forcings Γ in terms of maximalit...

1. Introduction Let V [G] be the result of adding a Cohen real and a Cohen subset of ω 2 to a model V of the GCH. Every infinite cardinal gets a new subset in V [G], namely, the Cohen real. Yet, in some sense, only ω and ω 2 get new subsets. One way to capture this is to say that a sort of dual to Covering holds between V and V [G], namely, " κ-cocovering " for κ other than ω and ω 2. We need s...