Related papers: The Approachability Ideal Without a Maximal Set
Let A be a locally m-convex Fr\'echet algebra. We give a necessary and sufficient condition for a cyclic Fr\'echet A-module X=A_+/I to be strictly flat, generalizing thereby a criterion of Helemskii and Sheinberg. To this end, we introduce…
Combining creature forcing approaches from arXiv:1003.3425 and arXiv:1402.0367, we show that, under CH, there is a proper $\omega^\omega$-bounding poset with $\aleph_2$-cc that forces continuum many pairwise different cardinal…
The aim of these lectures is to give a short introduction to forcing. We will avoid metamathematical issues as much as possible and similarly we will avoid performing the actual construction of forcing. We assume familiarity with basic…
We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. We apply this method to construct a forcing (without using an inaccessible or amalgamation) that makes all definable sets of reals…
We show that under $\BMM$ and "there exists a Woodin cardinal$"$, the nonstationary ideal on $\omega_1$ can not be defined by a $\Sigma_1$ formula with parameter $A \subset \omega_1$. We show that the same conclusion holds under the…
We use the technique of "classical realizability" to build new models of ZF + DC in which R is not well ordered. This gives new relative consistency results, probably not obtainable by forcing. This gives also a new method to get programs…
The main result of this paper is a partial answer to [math.LO/9909115, Problem 5.5]: a finite iteration of Universal Meager forcing notions adds generic filters for many forcing notions determined by universality parameters. We also give…
Using a variation of Woodin's $\mathbb{P}_{\mathrm{max}}$ forcing, we force over a model of the Axiom of Determinacy to produce a model of ZFC containing a very strongly increasing sequence of length $\omega_{2}$ consisting of functions…
We give conditions ensuring that the Fatou set and the complement of the fast escaping set of an exponential polynomial $f$ have finite Lebesgue measure. Essentially, these conditions are designed such that $|f(z)|\ge\exp(|z|^\alpha)$ for…
We present two ways in which the model $L({\mathbb R})$ is canonical assuming the existence of large cardinals. We show that the theory of this model, with {\em ordinal} parameters, cannot be changed by small forcing; we show further that a…
We solve a long-standing open problem of Shelah regarding the \emph{Approachability Ideal} $I[\kappa^+]$. Given a singular cardinal $\aleph_\gamma$, a regular cardinal $\mu\in (\mathrm{cf}(\gamma),\aleph_\gamma)$ and assuming appropriate…
We apply the finite element cell-centered (FECC) scheme [2] to the solution of the nearly incompressible elasticity problem. By applying a technique of dual mesh, such a low-order finite element scheme can be constructed from any given mesh…
It is sometimes desirable in choiceless constructions of set theory that one iteratively extends some ground model without adding new sets of ordinals after the first extension. Pushing this further, one may wish to have models $V \subseteq…
The purpose of this paper is to study the notion of relative extreme amenability for pairs of topological groups. We give a characterization by a fixed point property on universal spaces. In addition we introduce the concepts of an…
We produce, relative to a ${\sf ZFC}$ model with a supercompact cardinal, a ${\sf ZFC}$ model of the Proper Forcing Axiom in which the nonstationary ideal on $\omega_1$ is $\Pi_1$-definable in a parameter from $H_{\aleph_2}$.
Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an $\omega_2$-Aronszajn tree, the $\omega_1$-approachability property fails, and every stationary subset of $\omega_2 \cap \mathrm{cof}(\omega)$…
Our aim is to improve the negative results i.e. non-existence of limit models, and the failure of the generic pair property from math.LO/0609636 to inaccessible lambda as promised there. The motivation is that in [Sh:F756] the positive…
Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of…
We show that it is consistent relative to ZF, that there is no well-ordering of $\mathbb{R}$ while a wide class of special sets of reals such as Hamel bases, transcendence bases, Vitali sets or Bernstein sets exists. To be more precise, we…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…