相关论文: Cox's Theorem Revisited

The purpose of this lecture is to describe the KAM theorem in its most basic form and to give a complete and detailed proof. This proof essentially follows the traditional lines laid out by the inventors of this theory, and the emphasis is…

We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.

In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.

We use probabilistic methods to prove that many Coxeter groups are incoherent. In particular, this holds for Coxeter groups of uniform exponent > 2 with sufficiently many generators.

We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining…

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently…

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…

The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of…

The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting from the appropriate…

This paper explores conditions of existence of different types of consistent tests. New links of these types of consistency are also established. The existence of discernible (strong consistent) tests follows from the existence of pointwise…

Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…

We study the equations of universal torsors on rational surfaces.

The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.

We review recent work that employs the framework of logical inference to establish a bridge between data gathered through experiments and their objective description in terms of human-made concepts. It is shown that logical inference…

We discuss twisted cohomology, not just for ordinary cohomology but also for $K$-theory and other exceptional cohomology theories, and discuss several of the applications of these in mathematical physics. Our list of applications is by no…

We present a short and self-contained proof of the choosability version of Brooks' theorem.

We discuss the (twisted) weak positivity theorem. We also treat some applications.

After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…

We give a counting based proof of the Graham Pollak Theorem