Related papers: The last forcing standing with diamonds

We give some sufficient and necessary conditions on a forcing notion Q for preserving the forcing notion ([omega]^{aleph_0},supseteq^*) is proper. They cover many reasonable forcing notions.

Assuming the Continuum Hypothesis, there is a compact first countable connected space of weight aleph_1 with no totally disconnected perfect subsets. Each such space, however, may be destroyed by some proper forcing order which does not add…

We prove that any countable support iteration formed with posets with $\omega_2$-p.i.c.\ has $\omega_2$-c.c., assuming CH in the ground model and assuming also that $\omega_1$ is not collapsed. This improves earlier results of Shelah by…

Recently, a novel fixed point operation has been introduced over certain non-monotonic functions between stratified complete lattices and used to give semantics to logic programs with negation and boolean context-free grammars. We prove…

We show that generalized eventually narrow sequences on a strongly inaccessible cardinal $\kappa$ are preserved under the Cummings-Shaleh non-linear iterations of the higher Hechler forcing on $\kappa$. Moreover assuming GCH,…

We present a coalgebraic generalisation of Fischer and Ladner's Propositional Dynamic Logic (PDL) and Parikh's Game Logic (GL). In earlier work, we proved a generic strong completeness result for coalgebraic dynamic logics without…

Large language models suffer from "hallucinations"-logical inconsistencies induced by semantic noise. We propose that current architectures operate in a "Metric Phase," where causal order is vulnerable to spontaneous symmetry breaking.…

The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique…

Solovay's arithmetical completeness theorem states that the modal logic of provability coincides with the modal logic $\mathbf{GL}$. Hamkins and L\"owe studied the modal logical aspects of set theoretic multiverse and proved that the modal…

Our main theorem is about iterated forcing for making the continuum larger than aleph_2. We present a generalization of math.LO/0303294 which is dealing with oracles for random, etc., replacing aleph_1, aleph_2 by lambda,lambda^+ (starting…

Dynamo action in planetary cores has been extensively studied in the context of convectively-driven flows. We show in this letter that mechanical forcings, namely tides, libration and precession, are also able to kinematically sustain a…

We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…

This is an overview about a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along $\omega_1$ is given. Then its direct limit satisfies ccc by…

We prove for any mu = mu^{< mu}< theta < lambda, lambda large enough (just strongly inaccessible Mahlo) the consistency of 2^mu = lambda-> [theta]^2_3 and even 2^mu = lambda-> [theta]^2_{sigma,2} for sigma < mu . The new point is that…

We study a family of variants of Jensen's\emph{subcomplete forcing axiom}, $\mathsf{SCFA}$ and \emph{subproper forcing axiom}, $\mathsf{SubPFA}$. Using these we develop a general technique for proving non-implications of $\mathsf{SCFA}$,…

The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the controlled shape equation that are necessary…

We prove rigidity results for large classes of corona algebras, assuming the Proper Forcing Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable $C^*$-algebras with the metric approximation property…

We consider a simple model of higher order, functional computation over the booleans. Then, we enrich the model in order to encompass non-termination and unrecoverable errors, taken separately or jointly. We show that the models so defined…

A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but with predicate abstraction mechanism and equality is considered. The models of LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible constants)…

We investigate properties of trees of height $\omega_1$ and their preservation under subcomplete forcing. We show that subcomplete forcing cannot add a new branch to an $\omega_1$-tree. We introduce fragments of subcompleteness which are…