Related papers: On a Theorem by Bezboruah & Shepherdson

A completeness conjecture is advanced concerning the free small-colimit completion P(A) of a (possibly large) category A. The conjecture is based on the existence of a small generating-cogenerating set of objects in A. We sketch how the…

For (finitary) deductive systems, we formulate a signature-independent abstraction of the \emph{weak excluded middle law} (WEML), which strengthens the existing general notion of an inconsistency lemma (IL). Of special interest is the case…

We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.

This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…

In this paper, we study a class of Banach spaces, called \phi-spaces. In a natural way, we associate a measure of weak compactness in such spaces and prove an analogue of Sadovskii fixed point theorem for weakly sequentially continuous…

We prove weak and strong convergence theorems for a double Krasnoselskij type iterative method to approximate coupled solutions of a bivariate nonexpansive operator F : C x C --> C, where C is a nonempty closed and convex subset of a…

Fix an odd prime $p$. The results in this paper are modeled after work of Hesselholt and Hesselholt-Madsen on the $p$-typical absolute de Rham-Witt complex in mixed characteristic. We have two primary results. The first is an exact sequence…

We generalize Kirchberg's weak exactness to inclusions of C*-algebras in von Neumann algebras and study some characterizations and permanence properties which are similar to those of exact groups. We then consider a similar condition to…

In this paper we prove that any Poisson structure on a sheaf of Lie algebroids admits a weak deformation quantization, and give a sufficient condition for such a Poisson structure to admit an actual deformation quantization. We also answer…

We present the converse to a higher dimensional, scale-invariant version of a classical theorem of F. and M. Riesz. More precisely, for $n\geq 2$, for an ADR domain $\Omega\subset \re^{n+1}$ which satisfies the Harnack Chain condition plus…

In this note, we present a puzzle. We prove that Zermelo-Fraenkel set theory is inconsistent by proving, using Zermelo-Fraenkel set theory, the false statement that any algorithm that determines whether any $n \times n$ matrix over $\mathbb…

The proof of Theorem 11 of the paper M. Scheepers, Remarks on countable tightness, Topology and its Applications 161 (2014), 407 - 432 relies on Lemma 10 of that paper. The offered proof of Lemma 10 had shortcomings, and I was recently…

In this paper, we demonstrate that if, for every $\kappa$-complete fine filter $F$ over $\mathcal{P}_{\kappa}\lambda$, the associated Namba forcing $\mathrm{Nm}(\kappa,\lambda,F)$ is semiproper, then $\square(\mu,{<}\aleph_1)$ fails for all…

Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…

We discuss two variations of Edwards' duality theorem. More precisely, we prove one version of the theorem for cones not necessarily containing all constant functions. In particular, we allow the functions in the cone to have a non-empty…

We compare several versions of the quantitative Schur property of Banach spaces. We establish their equivalence up to multiplicative constants and provide examples clarifying when the change of constants is necessary. We also give exact…

For a homomorphism f: A --> B of commutative rings, let D(A,B) denote Ker[Pic(A) --> Pic(B)]. Let k be a field and assume that A is a f.g. k-algebra. We prove a number of finiteness results for D(A,B). Here are four of them. 1: Suppose B is…

We prove that it is relatively consistent with $\mathrm{ZFC}$ that every strong measure zero subset of the real line is meager-additive while there are uncountable strong measure zero sets (i.e., Borel's conjecture fails). This answers a…

Harvey Friedman's $ \mathsf{WD} $ is a weak set theory given by the following non-logical axioms: $ \mathsf{(W)} \; \forall x y \, \exists z \, \forall u \left[ \, u \in z \leftrightarrow ( \, u \in x \; \vee \; u = y \, ) \, \right] $; $…

We prove a two weight theorem for alpha-fractional singular integrals in higher dimensions, assuming energy side conditions. We also show that reversal of the Energy Lemma fails for the vector Riesz transforms in the plane, as well as other…