Related papers: Forcing, genericity and CBERS
We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy…
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Frechetness, strong Frechetness,…
We extend the hierarchy of finite-dimensional Ellentuck spaces to infinite dimensions. Using uniform barriers $B$ on $\omega$ as the prototype structures, we construct a class of continuum many topological Ramsey spaces $\mathcal{E}_B$…
We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we…
We present a detailed general framework to describe the forcing $\tilde{\mathbb{E}}$, defined by Kellner, Shelah and Tan\u{a}sie to prove the consistency with ZFC of an alternative order of Cicho\'n's maximum. Our presentation is close to…
We study the interplay between properties of measures on a Boolean algebra A and forcing names for ultrafilters on A. We show that several well known measure theoretic properties of Boolean algebras (such as supporting a strictly positive…
In this paper we report on some new results concerning the behavior of forces between two equal circular electrodes with finite thickness. We show that for close electrodes different scenarios can result, depending on the thickness and on…
In these notes we present the method introduced by Neeman of generalized side conditions with two types of models. We then discuss some applications: the Friedman-Mitchell poset for adding a club in \omega_2 with finite conditions,…
In this paper, we investigate connections between structures present in every generic extension of the universe $V$ and computability theory. We introduce the notion of {\em generic Muchnik reducibility} that can be used to to compare the…
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…
We present three natural combinatorial properties for class forcing notions, which imply the forcing theorem to hold. We then show that all known sufficent conditions for the forcing theorem (except for the forcing theorem itself),…
We give a bound on embedding dimensions of geometric generic fibers in terms of the dimension of the base, for fibrations in positive characteristic. This generalizes the well-known fact that for fibrations over curves, the geometric…
We establish a quantitative homogenization result for an interface moving through a field of sufficiently sparse but possibly impenetrable random obstacles. From a physical viewpoint, such problems arise e.g. in the context of the motion of…
In this paper, we proved that, for a semi-stable fibration of a proper smooth surface to a proper smooth curve over a field of positive characteristic, if the generic fiber is ordinary, then the semi-positivity theorem holds. As an…
We introduce a new class of ultrafilters which generalizes the well-known class of simple $P$-point ultrafilters. We prove that for any well-founded $\sigma$-directed partial order $\mathbb{D}$ there is a mild forcing extension where there…
This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…
We answer Blass' question from 1989 of whether the inequality $\gu < \gro$ is strictly stronger than the filter dichotomy principle affirmatively. We show that there is a forcing extension in which every non-meagre filter on $\omega$ is…
Some models of combinatorial principles have been obtained by collapsing a huge cardinal in the case of the successors of regular cardinals. For example, saturated ideals, Chang's conjecture, polarized partition relations, and transfer…
We continue the investigation started in [Sh:1215] about the relation between the Keilser-Shelah isomorphism theorem and the continuum hypothesis. In particular, we show it is consistent that the continuum hypothesis fails and for any given…