相关论文: NNR Revisited

We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations…

We prove a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle $\textsf{IGMP}$, $\textsf{GMP}$ together with $2^\omega \le \omega_2$ is consistent with the existence of an…

The goal of this paper is to establish that it remains undecidable whether a sequent is provable in two systems in which a weakening rule for an exponential modality is completely omitted from classical propositional linear logic…

In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal $\kappa \ge \omega_2$, $\textsf{ISP}(\kappa)$ implies that $\textsf{SCH}$ holds above $\kappa$, and (3) forcing posets…

This article critically reappraises arguments in support of Cantor's theory of transfinite numbers. The following results are reported: i) Cantor's proofs of nondenumerability are refuted by analyzing the logical inconsistencies in…

Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN…

We introduce a generalization of stationary set reflection which we call "filter reflection", and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We prove the independence of filter reflection…

Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…

We study the ability of different classes of voting rules to induce agents to report their preferences truthfully, if agents want to avoid regret. First, we show that regret-free truth-telling is equivalent to strategy-proofness among…

It was realized early on that topologies can model constructive systems, as the open sets form a Heyting algebra. After the development of forcing, in the form of Boolean-valued models, it became clear that, just as over ZF any…

We prove that a large class of presaturated ideals at inaccessible cardinals can be de-saturated while preserving their presaturation, answering both a question of Foreman and of Cox and Eskew. We do so by iterating a generalized version of…

Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…

This article continues Roslanowski and Shelah math.LO/9906024 and 1105.6049 We introduce here yet another property of (<lambda)-strategically complete forcing notions which implies that their lambda-support iterations do not collapse…

We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemela and…

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…

This work, shows how propositional resolution can be generalized to obtain a resolution proof system for constrained pseudo-propositional logic (CPPL), which is an extension resulted from inserting the natural numbers with few constraints…

The paper deals with the problem of finding the best alternatives on the basis of pairwise comparisons when these comparisons need not be transitive. In this setting, we study a reinforcement urn model. We prove convergence to the optimal…

We present an information theoretic proof of the nonsignalling multiprover parallel repetition theorem, a recent extension of its two-prover variant that underlies many hardness of approximation results. The original proofs used de Finetti…

We present some results about generics for computable Mathias forcing. The $n$-generics and weak $n$-generics in this setting form a strict hierarchy as in the case of Cohen forcing. We analyze the complexity of the Mathias forcing…