Related papers: Namba forcing, weak approximation, and guessing

We give an exposition of an iteration theorem for iterating $(<\lambda)$-closed stationary $\lambda^+$-cc forcing with supports of size $<\lambda$ and preserving these two properties. We discuss the relation of this theorem with other…

A famous conjecture of Graham asserts that every set $A \subseteq \mathbb{Z}_p \setminus \{0\}$ can be ordered so that all partial sums are distinct. Although this conjecture was recently proved for sufficiently large primes by Pham and…

We obtain central limit theorems for stationary random fields employing a novel measure of dependence called $\theta$-lex weak dependence. We show that this dependence notion is more general than strong mixing, i.e., it applies to a broader…

We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.

We show that all finite powers of a Hausdorff space X do not contain uncountable weakly separated subspaces iff there is a c.c.c poset P such that 1_P forces that ``X is a countable union of 0-dimensional subspaces of countable weight.'' We…

We look for a parallel to the notion of ``proper forcing'' among lambda-complete forcing notions not collapsing lambda^+ . We suggest such a definition and prove that it is preserved by suitable iterations.

The concept of (stable) weak containment for measure-preserving actions of a countable group $\Gamma$ is analogous to the classical notion of (stable) weak containment of unitary representations. If $\Gamma$ is amenable then the Rokhlin…

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 analyze the forcing notion $\mathcal P$ of finite matrices whose rows consists of isomorphic countable elementary submodels of a given structure of the form $H_{\theta}$. We show that forcing with this poset adds a Kurepa tree $T$.…

We introduce the forcing property "almost strong properness" which sits between properness and strong properness. As an application, we introduce a simple forcing with finite conditions to force $\rm MRP$.

Recently we drew attention to the fact that most recent 5th force searches and tests of the weak equivalence principle (WEP) utilize only one or two pairs of test samples. We argue that, despite the great precision of these experiments, the…

In this paper, we propose a weak regularity principle which is similar to both weak K\"onig's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then…

Cai and Hemachandra used iterative constant-setting to prove that Few $\subseteq$ $\oplus$P (and thus that FewP $\subseteq$ $\oplus$P). In this paper, we note that there is a tension between the nondeterministic ambiguity of the class one…

We prove that if a measure distal action $\alpha$ of a countable group $\Gamma$ is weakly contained in a strongly ergodic probability measure preserving action $\beta$ of $\Gamma$, then $\alpha$ is a factor of $\beta$. In particular, this…

We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations…

We show the relative energy inequality for the compressible Navier-Stokes system driven by a stochastic forcing. As a corollary, we prove the weak-strong uniqueness property (pathwise and in law) and convergence of weak solutions in the…

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness…

We investigate a Coulomb gas in a potential satisfying a weaker growth assumption than usual and establish a large deviation principle for its empirical measure. As a consequence the empirical measure is seen to converge towards a…

Let \alpha be a countable ordinal and \P(\alpha) the collection of its subsets isomorphic to \alpha. We show that the separative quotient of the set \P (\alpha) ordered by the inclusion is isomorphic to a forcing product of iterated reduced…

We introduce a category whose objects are stationary set preserving complete boolean algebras and whose arrows are complete homomorphisms with a stationary set preserving quotient. We show that the cut of this category at a rank initial…