Related papers: Weak covering and the tree property

A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the…

Laver, and Woodin independently, showed that models of ${\rm ZFC}$ are uniformly definable in their set-forcing extensions, using a ground model parameter. We investigate ground model definability for models of fragments of ${\rm ZFC}$,…

A matching from a finite subset $A\subset\mathbb{Z}^n$ to another subset $B\subset\mathbb{Z}^n$ is a bijection $f : A \rightarrow B$ with the property that $a+f(a)$ never lies in $A$. A matching is called acyclic if it is uniquely…

Consider an a.e.c. (abstract elementary class), that is, a class K of models with a partial order refining inclusion (submodel) which satisfy the most basic properties of an elementary class. Our test question is trying to show that the…

It is consistent (relative to ZFC) that the union of max{b,g} many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of…

This paper is a sequel to \cite{Tz10}, where a local version of ZFC, LZFC, was introduced and examined and transitive models of ZFC with properties that resemble large cardinal properties, namely Mahlo and $\Pi_1^1$-indescribable models,…

In this paper we analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of $\mathcal{L}_{\kappa,\kappa}$. Using this equivalence we…

We investigate the generalized tree properties and guessing model properties introduced by Wei\ss\ and Viale, as well as natural weakenings thereof, studying the relationships among these properties and between these properties and other…

Let $\omega$ be a continuous weight on $\mathbb R^+$ and let $L^1(\omega)$ be the corresponding convolution algebra. By results of Gr{\o}nb{\ae}k and Bade & Dales the continuous derivations from $L^1(\omega)$ to its dual space…

We use the core model for sequences of measures to prove a new lower bound for the consistency strength of the failure of the SCH: THEOREM (i) If there is a singular strong limit cardinal $\kappa$ such that $2^\kappa > kappa^+$ then there…

Let $X$ be a Banach space and let $C$ be a closed convex bounded subset of $X$. It is proved that $C$ is weakly compact if, and only if, $C$ has the {it generic} fixed point property ($\mathcal{G}$-FPP) for the class of $L$-bi-Lipschitz…

The main aim of this paper is to define a weakest topology $\sigma$ on a linear topological space $(E, \tau)$ such that each $\delta$-continuous functional on $(E, \tau)$ is $\delta$-continuous functional on $(E, \sigma)$ and to find out…

We are interested in the possible sets of cardinalities of branches of Kurepa trees in models of $ZFC$ $+$ $CH$. In this paper we present a sufficient condition (for sets of cardinals) to be consistently the set of cardinalities of branches…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

We give an explicit example of a fibration $f \colon X \to Y$ between smooth projective varieties whose "orbifold base" $\Delta_f$ in the sense of Campana has the property that the induced morphism $X \to (Y, \Delta_f)$ is not a morphism of…

We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…

Starting from a stationary set of supercompact cardinals we find a generic extension in which the tree property holds at every regular cardinal between $\aleph_2$ and $\aleph_{\omega^2}$.

We prove a correspondence between $\kappa$-small fibrations in simplicial presheaf categories equipped with the injective or projective model structure (and left Bousfield localizations thereof) and relatively $\kappa$-compact maps in their…

We introduce a hierarchy of models of the Axiom of Determinacy called \emph{Nairian models}. Forcing over the simplest Nairian model, we obtain a model of ${\sf{ZFC}}+{\sf{MM^{++}}}(c)+\neg\square_{\omega_3}+\neg\square(\omega_3)$. Then,…

We show that if $\mathbb Z^3$ can be tiled by translated copies of a set $F\subseteq\mathbb Z^3$ of cardinality the square of a prime then there is a weakly periodic $F$-tiling of $\mathbb Z^3$, that is, there is a tiling $T$ of $\mathbb…