Related papers: Weak diamond and Galvin's property

We show that every inclusion of von Neumann algebras with a faithful normal conditional expectation has the weak relative Dixmier property. This answers a question of Popa \cite{Po99}. The proof uses an improvement of Ellis' lemma for…

We show that the forcing axiom for countably compact, $\omega_2$-Knaster, well-met posets is inconsistent. This is supplemental to an inconsistency result of Shelah and sets a new limit to the generalization of Martin's Axiom to the stage…

David Aspero asks on the possibility of having Forcing axiom FA_{aleph_2}(K), where K is the class of forcing notions preserving stationarity of subsets of aleph_1 and of aleph_2. We answer negatively, in fact we show the negative result…

Motivated by the Bloch-Beilinson conjectures, we formulate a certain covariant weak Lefschetz property for Chow groups. We prove this property in some special cases, using Kimura's nilpotence theorem.

We establish the test which allows to show that a mean does not admit a weak-Hardy property. As a result we prove that Hardy and weak-Hardy properties are equivalent in the class of homogeneous, symmetric, repetition invariant, and Jensen…

In this short note, we shall prove some observations regarding the connection between indestructible $\omega_1$-guessing models and the $\omega_1$-approximation property of forcing notions.

We introduce a weak division-like property for noncommutative rings: a nontrivial ring is fadelian if for all nonzero $a,x$ there exist $b,c$ such that $x=ab+ca$. We prove properties of fadelian rings, and construct examples of such rings…

For any countable group $\Gamma$ satisfying the ``weak Rohlin property'', and for any dynamical property, the set of $\Gamma$-actions with that property is either residual or meager. The class of groups with the weak Rohlin property…

We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on $\kappa$, if $\kappa$ is…

We define a new approximation property for tracial von Neumann algebras, called \textit{weakly mixing approximation property} which, for discrete groups and II$_1$ factors, is equivalent to the negation of Kazhdan's property (T).

A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on…

Let F_q be the finite field with q elements. Consider the standard embedding GL(n,F_q) -> GL(n+1,F_q). In this paper we prove that for every irreducible representation pi of GL(n+1,F_q) over algebraically closed fields of characteristic…

The second author has recently shown ([20]) that any selectively (a) almost disjoint family must have cardinality strictly less than $2^{\alpeh_0}$, so under the Continuum Hypothesis such a family is necessarily countable. However, it is…

We show that an Artinian quotient of K[x, y, z] by an ideal I generated by powers of linear forms has the Weak Lefschetz property. If the syzygy bundle of I is semistable this follows from results of Brenner-Kaid; our proof works without…

In this note, we prove that the Daugavet property implies the polynomial Daugavet property, solving a longstanding open problem in the field. Our approach is based on showing that a geometric characterization of the Daugavet property due to…

In this paper, we introduce a very weak square principle which is even weaker than the similar principle introduced by Foreman and Magidor. A characterization of this principle is given in term of sequences of elementary submodels of…

In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.

The purpose of this note is to characterize the finite Hilbert functions which force all of their artinian algebras to enjoy the Weak Lefschetz Property (WLP). Curiously, they turn out to be exactly those (characterized by Wiebe in $[Wi]$)…

Viale \cite{Viale_GuessingModel} introduced the notion of Generic Laver Diamond at $\kappa$---which we denote $\Diamond_{\text{Lav}}(\kappa)$---asserting the existence of a single function from $\kappa \to H_\kappa$ that behaves much like a…

Justin Moore's weak club-guessing principle $\mho$ admits various possible generalizations to the second uncountable cardinal. One of them was shown to hold in ZFC by Shelah. A stronger one was shown to follow from several consequences of…