Related papers: All you need is $\mathbf{A}_\kappa$

We discuss the rainbow Ramsey theorems at limit cardinals and successors of singular cardinals, addressing some questions in \cite{MR2354904} and \cite{MR2902230}. In particular, we show for inaccessible $\kappa$,…

For a complete noncompact connected Riemannian manifold with bounded geometry, we prove a compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit…

Assume $AD+V=L(\mathbb{R})$. Let $\kappa=\utilde{\delta}^2_1$, the supremum of all $\utilde{\Delta}^2_1$ prewellorderings. We prove that extenders on the sequence of $\H$ that have critical point $\kappa$ are generated by countably complete…

We initiate the study of the spectrum $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(T)$ of a normal $\kappa$-tree $T$. The latter is an invariant in the sense that if $T$ and $T'$ are club-isomorphic, then the…

Let $\mathfrak{g}$ be a simple Lie algebra, and let $W_\kappa$ be the affine ${W}$-algebra associated to a principal nilpotent element of $\mathfrak{g}$ and level $\kappa$. We explain a duality between the categories of smooth ${W}$ modules…

We reprove and generalize the result that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a…

M. Goresky, G. Harder, and R. MacPherson defined weighted cohomologies of arithmetic groups \Gamma in a real group G, with coefficients in certain local systems, associated to arbitrary upper and lower weight profiles. The author shows,…

We give a combinatorial characterization of when a maximal almost disjoint family of a weakly compact cardinal $\kappa$ is indestructible by the higher random forcing $\mathbb Q_\kappa$. We then use this characterisation to show that…

We observe that the notions of a topological space being extremally disconnected, and of a continuous map of compact Hausdorff spaces being proper, and being surjective proper, can each be defined in terms of the Quillen lifting property…

We prove vanishing results of the cohomology groups of Aomoto complex over arbitrary coefficient ring for real hyperplane arrangements. The proof is using minimality of arrangements and descriptions of Aomoto complex in terms of chambers.…

We study the homotopy groups of complements to reducible divisors on non-singular projective varieties with ample components and isolated non normal crossings. We prove a vanishing theorem generalizing conditions for commutativity of the…

The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions and are consistent with the pointed measured…

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…

Let $X$ and $Y$ be compact Hausdorff spaces and suppose that there exists a linear continuous surjection $T:C_{p}(X) \to C_{p}(Y)$, where $C_{p}(X)$ denotes the space of all real-valued continuous functions on $X$ endowed with the pointwise…

In this paper we investigate more characterizations and applications of $\delta$-strongly compact cardinals. We show that, for a cardinal $\kappa$ the following are equivalent: (1) $\kappa$ is $\delta$-strongly compact, (2) For every…

We discuss a conjecture of Wilson that under the proper forcing axiom, $\Theta_0$ of the derived model at $\kappa$ is below $\kappa^+$. We prove the conjecture holds for the old derived model. Assuming mouse capturing in the new derived…

We prove that the moduli space of gauge equivalence classes of symplectic vortices with uniformly bounded energy in a compact Hamiltonian manifold admits a Gromov compactification by polystable vortices. This extends results of Mundet i…

We show that a strong form of the so called Lindstrom's Theorem fails to generalize to extensions of L_{kappa,omega} and L_{kappa,kappa}: For weakly compact kappa there is no strongest extension of L_{kappa,omega} with the…

Given a weakly compact cardinal $\kappa$, we give an axiomatization of intuitionistic first-order logic over $\mathcal{L}_{\kappa^+, \kappa}$ and prove it is sound and complete with respect to Kripke models. As a consequence we get the…

Let $C$ be a unital AH-algebra and $A$ be a unital simple C*-algebra with tracial rank zero. It has been shown that two unital monomorphisms $\phi, \psi: C\to A$ are approximately unitarily equivalent if and only if $$ [\phi]=[\psi] {\rm…