Related papers: Forcing with Adequate Sets of Models as Side Condi…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
We study L\"owenheim-Skolem and Omitting Types theorems in Transition Algebra, a logical system obtained by enhancing many sorted first-order logic with features from dynamic logic. The sentences we consider include compositions, unions,…
The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints :…
We study nested conditions, a generalization of first-order logic to a categorical setting, and provide a tableau-based (semi-decision) procedure for checking (un)satisfiability and finite model generation. This generalizes earlier results…
We present a method for iterating semiproper forcing which uses side conditions and is inspired by the technique recently introduced by Neeman.
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
We discuss some highlights of our computer-verified proof of the construction, given a countable transitive set-model $M$ of $\mathit{ZFC}$, of generic extensions satisfying $\mathit{ZFC}+\neg\mathit{CH}$ and $\mathit{ZFC}+\mathit{CH}$.…
Answering a question of Harrington, we show that there exists a proper forcing notion, which adds a minimal real $\eta \in \prod_{i<\omega} n^*_i$, which is eventually different from any old real in $\prod_{i<\omega} n^*_i$, where the…
In this paper we solve the satisfiability problem of an extended fragment of set computable theory which "forces the infinity" by a fruitful use of the witness small model property and the theory of formative processes.
Motivated in part by an observation that the zero forcing number for the complement of a tree on $n$ vertices is either $n-3$ or $n-1$ in one exceptional case, we consider the zero forcing number for the complement of more general graphs…
We consider the modality "$\varphi$ is true in every $\sigma$-centered forcing extension", denoted $\square\varphi$, and its dual "$\varphi$ is true in some $\sigma$-centered forcing extension", denoted $\lozenge\varphi$ (where $\varphi$ is…
The foundations of forcing theory are reworked to streamline the presentation and to show how the most basic results are applicable in very general contexts.
The technique of "classical realizability" is an extension of the method of "forcing"; it permits to extend the Curry-Howard correspondence between proofs and programs, to Zermelo-Fraenkel set theory and to build new models of ZF, called…
We consider a six dimensional gauge theory compactified on $T^2/\mathbb{Z}_2$ with magnetic flux. The configurations of models are classified by winding numbers at the fixed points. Requiring the existence of generation numbers and Yukawa…
This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.
We study the spectrum of forcing notions between the iterations of $\sigma$-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of $\alpha$-proper forcings for indecomposable countable ordinals as well as…
We apply Neeman's method of forcing with side conditions to show that PFA does not imply the precipitousness of the nonstationary ideal on $\omega_1$.
By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal…
We develop a unified framework for iterated symmetric extensions with countable support and, more generally, with $<\kappa$-support. Set-length iterations are treated uniformly, and when the iteration template is first-order definable over…
In the present paper we are interested in properties of forcing notions which measure in a sense the distance between the ground model reals and the reals in the extension. We look at the ways the ``new'' reals can be aproximated by ``old''…