Related papers: Bounded forcing axioms and Baumgartner's conjectur…

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

We answer a question of Moore by building a forcing extension satisfying measuring together with CH. The construction works over any model of ZFC and can be described as a forcing iteration with countable structures as side conditions and…

We show if we use countable support iteration of forcing notions not adding reals that satisfy additional conditions, then the limit forcing does not add reals. As a result we prove that we can amalgamate two earlier methods and prove the…

We develop a forcing framework based on the idea of amalgamating language fragments into a theory with a canonical term model. We then demonstrate the usefulness of this framework by applying it to variants of the extended Namba problem, as…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

We describe a formalization of forcing using Boolean-valued models in the Lean 3 theorem prover, including the fundamental theorem of forcing and a deep embedding of first-order logic with a Boolean-valued soundness theorem. As an…

We lay the ground for an Isabelle/ZF formalization of Cohen's technique of forcing. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize the definition of forcing notions as…

We present a sufficient condition for irreducibility of forcing algebras and study the (non)-reducedness phenomenon. Furthermore, we prove a criterion for normality for forcing algebras over a polynomial base ring with coefficients in a…

We introduce a new and natural stationary set preserving forcing $\mathbb P^{c-c}({\lambda},{\mu})$ that (under $\mathsf{NS}_{\omega_1}$ precipitous + existence of $H_{\theta}^#$ for a sufficiently large regular ${\theta}$) increases the…

The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, interpreting necessity as "in all forcing extensions" and possibility as "in some forcing extension". In this modal…

Assume $\kappa = \kappa^{< \kappa}$ (usually $\aleph_0$ or an inaccessible). We shall deal with iterated forcings preserving ${}^{\kappa>}{\rm Ord}$ and not collapsing cardinals along a linear order $L$. A sufficient condition for this,…

We show unexpected connection of Set Theoretical Forcing with Quantum Mechanical lattice of projections over some separable Hilbert space. The basic ingredient of the construction is the rule of indistinguishability of Standard and some…

We prove that the forcing axiom $MA^{1.5}_{\aleph_2}(\mbox{stratified})$ implies $\Box_{\omega_1, \omega_1}$. Using this implication, we show that the forcing axiom $MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$ is inconsistent. We also derive weak…

The separation between two theorems in reverse mathematics is usually done by constructing a Turing ideal satisfying a theorem P and avoiding the solutions to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a forcing…

In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of the generalised Cantor space and study its associated ideal of null sets and notion of measurability. This issue was…

We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three…

We introduce the forcing property of descending distributivity. A forcing $\mathbb{P}$ is $\kappa$-descending distributive if for all decreasing sequences $(D_\alpha)_{\alpha<\kappa}$ of open dense sets, $\bigcap_\alpha D_\alpha$ is open…

In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to $\omega_1$-sequences of the selection principle and…

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…

We show that the forcing axiom for countably compact, $\omega_2$-Knaster, well-met posets is inconsistent. This is supplemental to an inconsistency result of Shelah and sets a new limit to the generalization of Martin's Axiom to the stage…