Related papers: On the centeredness of saturated ideals

In this article we prove two cases of the abundance conjecture for $3$-folds in characteristic $p>5$: $(i)$ $(X, \Delta)$ is KLT and $\kappa(X, K_X+\Delta)=1$, and $(ii)$ $(X, 0)$ is KLT, $K_X\equiv 0$ and $X$ is not uniruled.

We discuss the space $VPS(Q,H)$ of ideals with Hilbert function $H=(1,n,n, \ldots)$ that are apolar to a full rank quadric $Q$. We prove that its components of saturated ideals are closely related to the locus of Gorenstein algebras and to…

We give another proof that for every lambda >= beth_omega for every large enough regular kappa < beth_omega we have lambda^{[kappa]}= lambda, dealing with sufficient conditions for replacing beth_omega by aleph_omega. In section 2 we show…

We discuss the generalized Kurepa hypothesis $KH_{\lambda}$ at singular cardinals $\lambda$. In particular, we answer questions of Erd\"{o}s-Hajnal [1] and Todorcevic [6], [7] by showing that $GCH$ does not imply $KH_{\aleph_\omega}$ nor…

A characteristic result is that if 2^{aleph_0}< mu < mu^+< lambda = cf(lambda)< mu^{aleph_0}, then among the separable reduced p-groups of cardinality lambda which are (< lambda)-stable there is no universal one.

We consider several variants of Keisler's isomorphism theorem. We separate these variants by showing implications between them and cardinal invariants hypotheses. We characterize saturation hypotheses that are stronger than Keisler's…

We describe some (countably many) classes K^{n,e} of finite graphs and prove that if lambda^{aleph_0}= lambda then every lambda^+-chromatic graph of cardinal lambda^+ contains, for some n, e, all members of K^{n,e} as subgraphs. On the…

We show that if the real line is the disjoint union of kappa meager sets such that every meager set is contained in a countable union of them, then kappa = omega_1. This answers a question addressed by J. Cichon. We also prove two theorems…

We show that the reduced cofinality of the nonstationary ideal NS_kappa on a regular uncountable cardinal kappa may be less than its cofinality, where the reduced cofinality of NS_kappa is the least cardinality of any family F of…

Let $\mathscr{F}=(F_n)$ be a sequence of nonempty finite subsets of $\omega$ such that $\lim_n |F_n|=\infty$ and define the ideal $$\mathcal{I}(\mathscr{F}):=\left\{A\subseteq \omega: |A\cap F_n|/|F_n|\to 0~\mbox{as}~n\to \infty \right\}.$$…

We study limit models in the abstract elementary class of modules with embeddings as algebraic objects. We characterize parametrized noetherian rings using the degree of injectivity of certain limit models. We show that the number of limit…

We continue work on the topology obtained by the convergence $\lambda_{ls}$, which started in \cite{KuPaCZ}, and further investigated in \cite{KuPaFil19}. The main goal is to describe the closed sets and closure operator by the family of…

In this paper, we investigate some topics around the closed image $S$ of a rational map $\lambda$ given by some homogeneous elements $f_1,...,f_n$ of the same degree in a graded algebra $A$. We first compute the degree of this closed image…

We study the properties of $\text{CAT}(\kappa)$ surfaces: length metric spaces homeomorphic to a surface having curvature bounded above in the sense of satisfying the $\text{CAT}(\kappa)$ condition locally. The main facts about…

We find many conditions equivalent to the model-theoretical property $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in [L1]. Our conditions involve uniformity of ultrafilters, compactness properties of products of topological…

We study the approachability ideal I[\kappa^+] in the context of large cardinals properties of the regular cardinals below a singular \kappa. As a guiding example consider the approachability ideal I[\aleph_{\omega+1}] assuming that…

Being motivated by the problem of deducing $L^p$-bounds on the second fundamental form of an isometric immersion from $L^p$-bounds on its mean curvature vector field, we prove a (nonlinear) Calder\'on-Zygmund inequality for maps between…

We introduce and study certain notions which might serve as substitutes for maximum density packings and minimum density coverings. A body is a compact connected set which is the closure of its interior. A packing $\cal P$ with congruent…

In this paper we address a problem posed by Shelah in 1999 to find a suitable notion for superstability for abstract elementary classes in which limit models of cardinality $\mu$ are saturated. Theorem 1. Suppose that $\mathcal{K}$ is a…

We prove that a large class of presaturated ideals at inaccessible cardinals can be de-saturated while preserving their presaturation, answering both a question of Foreman and of Cox and Eskew. We do so by iterating a generalized version of…