Easton proved that the behavior of the exponential function 2 at regular cardinals κ is independent of the axioms of set theory except for some simple classical laws. The Singular Cardinals Hypothesis SCH implies that the Generalized Continuum Hypothesis GCH 2 = κ holds at a singular cardinal κ if GCH holds below κ. Gitik and Mitchell have determined the consistency strength of the negation of ...

The paper reviews special Aronszajn trees, both at ω1 and κ + for an uncountable regular κ. It provides a comprehensive classification of the trees and discusses the existence of these trees under different set-theoretical assumptions. The paper provides details and proofs for many folklore results which circulate (often without a proper proof) in the literature.

If B is a compact space and B \ {pt} is Lindelöf then Bκ \ { − → pt} is star-Linedlöf for every κ. If B \ {pt} is compact then Bκ \ { − → pt} is discretely star-Lindelöf. In particular, this gives new examples of Tychonoff discretely star-Lindelöf spaces with unlimited extent.

The subalgebra of the tautological ring of the moduli of curves of compact type generated by the κ classes is studied in all genera. Relations, constructed via the virtual geometry of the moduli of stable quotients, are used to obtain minimal sets of generators. Bases and Betti numbers of the κ rings are computed. A universality property relating the higher genus κ rings to the genus 0 rings is...

It is proved that given H ≥ 0 and an embedded compact orientable constant mean curvature H surface M included in the half space z ≥ 0, not everywhere tangent to z = 0 along its boundary ∂M = γ ⊂ {z = 0}, the inequality H ≤ (min κ) ( min √ 1 − (κg/κ) ) is satisfied, where κ and κg are the geodesic curvatures of γ on z = 0 and on the surface M , respectively, if and only if M is a spherical cap o...

The Lipschitz and C harmonic capacities κ and κc in R n can be considered as high-dimensional versions of the so-called analytic and continuous analytic capacities γ and α (respectively). In this paper we provide a dual characterization of κc in the spirit of the classical one for the capacity α by means of the Garabedian function. Using this new characterization, we show that κ(E) = κ(∂oE) for...

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...

In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...

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 ...

I use generic embeddings induced by generic normal measures on Pκ(λ) that can be forced to exist if κ is an indestructibly weakly compact cardinal. These embeddings can be used in order to obtain the forcing axioms MA(<μ-closed) in forcing extensions. This has consequences in V: The singular cardinal hypothesis holds above κ, and κ has a useful Jónsson-like property. This, in turn, implies that...