Related papers: Bounded Namba forcing axiom may fail
The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved…
We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using our method we prove that the forcing axiom for the class of all the small finitely proper posets is compatible with a…
We prove that the local version of the chain rule cannot hold for the fractional variation defined in arXiv:1809.08575. In the case $n = 1$, we prove a stronger result, exhibiting a function $f \in BV^{\alpha}(\mathbb{R})$ such that $|f|…
We show how to force, with finite conditions, the forcing axiom PFA(T), a relativization of PFA to proper forcing notions preserving a given Souslin tree T. The proof uses a Neeman style iteration with generalized side conditions consisting…
We prove that if there exists a simplified $(\omega_1,2)$-morass, then there is a ccc forcing which adds an $\omega_3$-chain in P($\omega_1$) mod finite and a ccc forcing which adds a family of $\omega_3$-many strongly almost disjoint…
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 present a general framework for forcing on $\omega_2$ with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial…
Suppose that $T^*$ is an $\omega_1$-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA($T^*$) for proper forcings which preserve these properties of $T^*$. We prove that PFA($T^*$) implies many of the strong…
In chapter 9 of his book "The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal", Woodin shows how to force the Strong Chang Conjecture over models of determinacy using $\mathbb{P}_{\mathrm{max}}$. We show here how a…
Shelah considered a certain version of Strong Chang's Conjecture, which we denote $\text{SCC}^{\text{cof}}$, and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an…
Recently the second author introduced combinatorial principles that characterize supercompactness for inaccessible cardinals but can also hold true for small cardinals. We prove that the proper forcing axiom PFA implies these principles…
We suggest a forcing version of Yablo's paradox and discuss its implication on self-reference.
In this paper, we explore various ways in which a factor $\sigma$-algebra $\mathscr{B}$ can sit in a dynamical system $\mathbf{X} :=(X, \mathscr{A}, \mu, T)$, i.e. we study some possible structures of the extension $\mathscr{A} \rightarrow…
The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping…
Throughout this abstract let U be a fixed p-point ultrafilter and let I be the dual ideal. Grigorieff forcing is P(U)={p:omega to 2|dom(p) is an element of I} ordered by reverse inclusion. It is well known that Grigorieff forcing is proper.…
We show that it is equiconsistent with $\mathsf{ZF}$ that Fodor's lemma fails everywhere, and furthermore that the club filter on every regular cardinal is not even $\sigma$-complete. Moreover, these failures can be controlled in a very…
We show that compact cardinals and {\rm MM} are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding 'regressive' $\lambda$-Kurepa-trees in either case. We argue that the destruction of regressive…
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain $\Omega $ can be extended, under suitable conditions, to the case in which the…
We show that higher Sacks forcing at a regular limit cardinal and club Miller forcing at an uncountable regular cardinal both add a diamond sequence. We answer the longstanding question, whether $\kappa = \kappa^{<\kappa} \geq\aleph_1$…
We analyse the Boolean-valued random forcing $B_{M,\Omega}$ in bounded arithmetics developed in Krajicek (Forcing with random variables and proof complexity, vol. 382, Cambridge University Press, 2011) from the perspective of the forcing in…