Related papers: Reflection principles, GCH and the uniformization …
The relationship between the large cardinal notions of strong compactness and supercompactness cannot be determined under the standard ZFC axioms of set theory. Under a hypothesis called the Ultrapower Axiom, we prove that the notions are…
We use reverse mathematics to analyze "iterated jump" versions of the following four principles: the atomic model theorem with subenumerable types (AST), the diagonally noncomputable principle (DNR), weak weak K\H{o}nig's lemma (WWKL), and…
We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however.…
We consider some natural generalizations to the class of all GLP-algebras of the so-called reduction property for reflection algebras in arithmetic. An analogue of this property is established for the free GLP-algebras and for some…
The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are…
We present a general framework for carrying out some constructions. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which…
We continue [GbSh:568] (math.LO/0003164), proving a stronger result under the special continuum hypothesis (CH). The original question of Eklof and Mekler related to dual abelian groups. We want to find a particular example of a dual group,…
Primitive recursion, mu-recursion, universal object and universe theories, complexity controlled iteration, code evaluation, soundness, decidability, G\"odel incompleteness theorems, inconsistency provability for set theory, constructive…
We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on…
Recently Alan D. Sokal gave a very short and completely elementary proof of the uniform boundedness principle. The aim of this note is to point out that by using a similiar technique one can give a considerably short and simple proof of a…
The purpose of this paper is to introduce the concept of reflecting numbers to the realm of number theory and to classify reflecting numbers of certain types. For us, reflecting numbers are coming from congruent numbers, above congruent…
This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual…
This paper aims at comparing two coupling approaches as basic layers for building clustering criteria, suited for modularizing and clustering very large networks. We briefly use "optimal transport theory" as a starting point, and a way as…
Recently the second author introduced combinatorial principles that characterize supercompactness for inaccessible cardinals but can also hold true for small cardinals. We prove that the proper forcing axiom PFA implies these principles…
Superpositions of coherent light waves typically interfere. We present superpositions of up to six plane waves which defy this expectation by having a perfectly homogeneous mean square of the electric field. For many applications in optics…
Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection…
The detection of entanglement in a bipartite state is a crucial issue in quantum information science. Based on realignment of density matrices and the vectorization of the reduced density matrices, we introduce a new set of separability…
Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to…
We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and $G_\delta$-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to…
It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical…