Related papers: Small u_kappa and large 2^kappa for supercompact k…
We extend the normalization results of the author's paper "Full normalization for transfinite stacks" [5] to mice at the level of $\kappa^+$-supercompactness: given a normal iteration strategy $\Sigma$ for such a mouse $M$, with both $M$…
We give some general criteria, when kappa-complete forcing preserves largeness properties -- like kappa-presaturation of normal ideals on lambda (even when they concentrate on small cofinalities). Then we quite accurately obtain the…
We answer a variant of a question of Rodl and Voigt by showing that, for a given infinite cardinal lambda, there is a graph G of cardinality kappa =(2^lambda)^+ such that for any colouring of the edges of G with lambda colours, there is an…
This paper studies cardinal invariants b_kappa and t_kappa, the natural generalizations of the invariants b and t to a regular cardinal kappa.
In the first part of the paper, we show that if $\omega \le \kappa < \lambda$ are cardinals, $\kappa^{<\kappa} = \kappa$, and $\lambda$ is weakly compact, then in $V[\M(\kappa,\lambda)]$ the tree property at $\lambda =…
We characterize the situation of small cardinality for a product of cardinals divided by an ultrafilter. We develop the notion of weak normality. We include an application to Boolean Algebras.
A strong coloring on a cardinal $\kappa$ is a function $f:[\kappa]^2\to \kappa$ such that for every $A\subseteq \kappa$ of full size $\kappa$, every color $\gamma<\kappa$ is attained by $f\upharpoonright[A]^2$. The symbol…
It is well-known that the consistency strength of the GCH failing at a measurable cardinal is the existence of a cardinal $\kappa$ with $o(\kappa)=\kappa^{++}$. As the literature does not contain more than a proof sketch of the lower bound…
In this paper we study a notion of a $\kappa$-covering in connection with Bernstein sets and other types of nonmeasurability. Our results correspond to those obtained by Muthuvel and Nowik. We consider also other types of coverings.
We show that the definition of caliber given by Engelking in R. Engelking, "General topology", Sigma series in pure mathematics, Heldermann, vol. 6, 1989, which we will call caliber*, differs from the traditional notion of this concept in…
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…
Given a Woodin cardinal $\delta$, I show that if $F$ is any Easton function with $F"\delta\subseteq\delta$ and $\GCH$ holds, then there is a cofinality-preserving forcing extension in which $2^\gamma= F(\gamma)$ for each regular cardinal…
In \cite{Chaber}, Chaber has proved that countably compact spaces with a quasi $G_{\delta }$-diagonal are compact. We prove that initially $\kappa $% -compact spaces with a quasi $G_{\kappa }$-diagonal are compact, for any infinite cardinal…
This document contains additional numerical and graphical evidence to support some of the conjectures mentioned in \cite{GM3}. We give more evidence for $\kappa=3,4$ in dimension 2. As mentioned in that article we still don't quite…
Recent experiments on mesoscopic samples and theoretical considerations lead us to analyze multiply charged ($n>1$) vortex solutions of the Ginzburg-Landau equations for arbitrary values of the Landau-Ginzburg parameter $\kappa$. For $n\gg…
We prove a revised version of Laver's indestructibility theorem which slightly improves over the classical result. An application yields the consistency of $(\kappa^+,\kappa)\notcc(\aleph\_1,\aleph\_0)$ when $\kappa$ is supercompact. The…
Let kappa be an uncountable cardinal and the edges of a complete graph with kappa vertices be colored with aleph_0 colors. For kappa >2^{aleph_0} the Erd\H{o}s-Rado theorem implies that there is an infinite monochromatic subgraph. However,…
It is shown that the Lame's equation ${d^{2}\over d z^{2}}X+\kappa^{2} cn^{2}(z, {1\over \sqrt 2})X=0$ can be reduced to the hyper-geometric equation. The characteristic exponents of this equation are expressed in terms of elementary…
We review various aspects of a fermionic gauge symmetry, known as the $\kappa$--symmetry, which plays an important role in formulations of superstrings, supermembranes and higher dimensional extended objects. We also review some aspects of…
We prove a weakened version of the reflection of Reinhardt cardinals by super Reinhardt cardinals: Let $M=(V^M,P)$ be a countable model of second order set theory $\mathsf{ZF}_2$ (with universe $V^M$ and classes $P$) which models "$\kappa$…