相关论文: G\"{o}del's incompleteness theorem and the Anti-Me…

In a recent publication [PRL 111, 160405 (2013)] we proved a version of Heisenberg's error-disturbance tradeoff. This result was in apparent contradiction to claims by Ozawa of having refuted these ideas of Heisenberg. In a direct reaction…

This article discusses what can be proved about the foundations of mathematics using the notions of algorithm and information. The first part is retrospective, and presents a beautiful antique, Godel's proof, the first modern incompleteness…

An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt G\"odel's modal ontological argument. Some argument premises are modified, others are dropped, modal…

This short squib looks at how using a broader definition of G\"odel numbering to mimic the accessibility relation between possible worlds results in two-world systems that sidestep undecidable sentences as well as the Liar paradox.

Godelian sentences of a sufficiently strong and recursively enumerable theory, constructed in Godel's 1931 groundbreaking paper on the incompleteness theorems, are unprovable if the theory is consistent; however, they could be refutable.…

This article gives a summary of the author's Ph.D. dissertation (arXiv:1609.06297). In addition to an overview of notions and results, it also provides sketches of various proofs and simplified presentations of certain abstract results of…

In our previous work "Characterization of certain homorphic geodesic cycles on Hermitian locally symmetric manifolds of the noncompact type" in "Modern methods in Complex Analysis" Annals of Math. Studies 138 (1995) 85-118, we formulated a…

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of \L ukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard…

MV-algebras are an algebraic semantics for Lukasiewicz logic and MV-algebras generated by a finite chain are Heyting algebras where the Godel implication can be written in terms of De Morgan and Moisil's modal operators. In our work, a…

In a previous article by two of the present authors and S. Bonzio, \L ukasiewicz near semirings were introduced and it was proven that basic algebras can be represented (precisely, are term equivalent to) as near semirings. In the same work…

This text has two parts; the first is the essentially unmodified text of the 1973-74 seminar of M. Lejeune-Jalabert and B. Teissier on integral dependence in complex analytic geometry with J-J. Risler's appendix on the Lojasiewicz exponents…

Hrushovski's generalization and application of [Jouanolou, "Hypersurfaces solutions d'une \'equation de Pfaff analytique", Mathematische Annalen, 232 (3):239--245, 1978] is here refined and extended to the partial differential setting with…

Let G be a finite graph with the non-k-order property (essentially, a uniform finite bound on the size of an induced sub-half-graph). A major result of the paper applies model-theoretic arguments to obtain a stronger version of…

We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.

These notes grew out of an expose on M. Gromov's paper "Convex sets and K\"ahler manifolds'' ("Advances in Differential Geometry and Topology,'' World Scientific, 1990) at the DMV-Seminar on "Combinatorical Convex Geometry and Toric…

This paper proves that protomechanics, previously introduced in quant-ph/9909025, deduces both quantum mechanics and classical mechanics. It does not only solve the problem of the arbitrariness on the operator ordering for the quantization…

We give examples of groups G such that G^00 is different from G^000. We also prove that for groups G definable in an o-minimal structure, G has a "bounded orbit" iff G is definably amenable. These results answer questions of Gismatullin,…

This work is motivated by the problem of finding the limit of the applicability of the first incompleteness theorem ($\sf G1$). A natural question is: can we find a minimal theory for which $\sf G1$ holds? We examine the Turing degree…

We give a proof of the inconsistency of PM arithmetic, classical set theory and related systems, incidentally exposing an error in Goedel's own proof of Goedel's Theorems. The inconsistency proof, that formulae of the form R and ~R occur as…

A Hilbert-type axiomatic rejection $\mathbf{HAR}$ for the propositional fragment $\mathbf{L_1}$ of Le\'{s}niewski's ontology is proposed. Also a Gentzen-type axiomatic rejection $\mathbf{GAR}$ of $\mathbf{L_1}$ is proposed. Models for…