Related papers: On an example of LaBuz

When formalized, some diagonal arguments do not show the diagonal object to be impossible but rather reveal some other anomaly (e.g., that one of the relevant sets is ill-defined). This raises the possibility that some diagonal arguments…

Let B_n denote the nth Bell number. We use well-known recursive expressions for B_n to give a generalizing recursion that can be used to prove Touchard's congruence.

The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first $L_p$-cohomology of…

The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations…

It is well known that there is no basis of the field for real numbers regarded as a vector space over any proper subfield that is closed under multiplication. Mabry has extended this result to bases of arbitrary proper field extensions. The…

This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…

The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible…

In order to study the Yamabe changing-sign problem, Bahri and Xu proposed a conjecture which is a universal inequality for $p$ points in $\mathbb R^m$. They have verified the conjecture for $p\leq3$. In this paper, we first simplify this…

We show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure mu on [-1,1]. Assume that mu is a regular measure, and is absolutely continuous in an open…

The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver's theorem and Bukovsk\'y's theorem assert that set-generic extensions of a given…

Let N be a normal subgroup of a finite group G. Let N\le H\le G such that N has a complement in H and (|N|,|G:H|)=1. If N is abelian, a theorem of Gasch\"utz asserts that N has a complement in G as well. Brandis has asked whether the…

We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.

Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. In this paper I restate and analyze…

Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…

One of the key assumptions of the Standard Model of fundamental particles is that the interactions of the charged leptons, namely electrons, muons, and taus, differ only because of their different masses. While precision tests comparing…

We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…

We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics for conditionals founded on a calculus of intervention, and axiomatization of causal reasoning for…

The ground axiom is the assertion that the set-theoretic universe is not obtainable by forcing over any inner model. Although this appears at first to be a second-order assertion, it is actually first-order expressible in the language of…

Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.

For $m=3,4,\ldots$ those $p_m(x)=(m-2)x(x-1)/2+x$ with $x\in\mathbb Z$ are called generalized $m$-gonal numbers. Sun [13] studied for what values of positive integers $a,b,c$ the sum $ap_5+bp_5+cp_5$ is universal over $\mathbb Z$ (i.e., any…