Related papers: Comparing forcing approaches to dense ideals

Selected issues of the concept of spontaneous collapse are discussed, with the emphasis on the gravity-related model. We point out that without spontaneous collapses the Schr\"odinger cat states would macroscopically violate the standard…

We consider the incidence structure formed by the twelve pentagons given by the vertex neighborhoods of the icosahedron. Interpreting this structure purely in terms of coplanarity conditions, we show that -- up to projective equivalence --…

Smallish large cardinals $\kappa$ are often characterized by the existence of a collection of filters on $\kappa$, each of which is an ultrafilter on the subsets of $\kappa$ of some transitive $\mathrm{ZFC}^-$-model of size $ \kappa$. We…

Spontaneous collapse models aim to solve the long-standing measurement problem in quantum mechanics by modifying the theory's dynamics to include objective wave function collapses. These collapses occur randomly in space, bridging the gap…

The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…

We present a forcing for blowing up 2^lambda and making ``many positive polarized partition relations'' (in a sense made precise in (c) of our main theorem) hold in the interval [lambda, 2^lambda]. This generalizes results of [276], Section…

This is a continuation of the paper [J. Symb. Log. 87 (2022), 1065--1092]. For an ideal $\mathcal{I}$ on $\omega$ we denote $\mathcal{D}_{\mathcal{I}}=\{f\in\omega^\omega: f^{-1}[\{n\}]\in\mathcal{I} \text{ for every $n\in \omega$}\}$ and…

We investigate two variants of splitting tree forcing, their ideals and regularity properties. We prove connections with other well-known notions, such as Lebesgue measurablility, Baire- and Doughnut-property and the Marczewski field.…

We study higher dimensional gravitational collapse to topological black holes in two steps. Firstly, we construct some (n+2)-dimensional collapsing space-times, which include generalised Lemaitre-Tolman-Bondi-like solutions, and we prove…

We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…

We provide solutions to several problems of Foreman about ideals, several of which are closely related to Mitchell's notion of \emph{strongly proper} forcing. We prove: 1) Presaturation of a normal ideal implies projective antichain…

This paper continues the study of the Ramsey-like large cardinals. Ramsey-like cardinals are defined by generalizing the characterization of Ramsey cardinals via the existence of elementary embeddings. Ultrafilters derived from such…

We complete our previous study of critical gravitational collapse in the axion-dilaton system by analysing the hyperbolic and parabolic ans\"atze. As could be expected, the corresponding Choptuik exponents in four-dimensions differ from the…

We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new…

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…

We carry out numerical simulations of the gravitational collapse of a perfect fluid with the ultrarelativistic equation of state $P=\kappa\rho$, in spherical symmetry in $2+1$ spacetime dimensions with $\Lambda<0$. At the threshold of…

Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call ${\rm GM}^+(\omega_3,\omega_1)$ holds. This principle implies ${\rm ISP}(\omega_2)$ and ${\rm ISP}(\omega_3)$, and…

We share both recent and older, well-known results regarding the notions of stable ordinals and shrewd cardinals. We then argue that $\Sigma_2$-nonprojectible ordinals may be considered as recursive analogues to subtle cardinals, a highly…

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket…

In analogy to the skeletons of a simplicial complex and their Stanley--Reisner ideals we introduce the skeletons of an arbitrary monomial ideal $I\subset S=K[x_1,...,x_n]$. This allows us to compute the depth of $S/I$ in terms of its…