Related papers: Remarks on an article by Rabern et al
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
G\"odel's argument for the First Incompleteness Theorem is, structurally, a proof by contradiction. This article intends to reframe the argument by, first, isolating an additional assumption the argument relies on, and then, second, arguing…
We give a new proof of a version of the main theorem of the previous paper in the series about embedding of an algebraic system into ultraproducts.
General considerations on the Equivalence conjectures and a review of few mathematical results.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
We prove some constructive results that on first and maybe even on second glance seem impossible.
We study the Fibered Isomorphism Conjecture of Farrell and Jones in L-theory for groups acting on trees. In several cases we prove the conjecture. This includes wreath products of abelian groups and free metabelian groups. We also deduce…
We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.
This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.
The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.
We make remarks on Ristroph and Zhang's [{\it Phys. Rev. Lett.} {\bf 101}, 194502 (2008)] paper. We argue especially that due to the interferences the calibration procedures in [1] were not complete and this will induce some measurements'…
We prove part of the conjectures in [Li10a] (arXiv:1007.5384). We also relate the construction of quantum modified algebras in [Li10a] with the functorial construction in [ZH08](arXiv:0803.3668).
The Jacobian conjecture in dimension $n$ asserts that any polynomial endomorphism of $n$-dimensional affine space over a field of zero characteristic, with the Jacobian equal 1, is invertible. The Dixmier conjecture in rank $n$ asserts that…
This article describes recent work on the topic of specifying properties of transition systems. By giving a suitably abstract description of transition systems as coalgebras, it is possible to derive logics for capturing properties of these…
We prove a conjecture of Gao and Kitaev on Wilf-equivalence of sets of patterns {12345,12354} and {45123,45213} that extends the list of 10 related conjectures proved in the literature in a series of papers. To achieve our goals, we prove…
Alexander L. Rosenberg has constructed a spectrum for abelian categories which is able to reconstruct a quasi-separated scheme from its abelian category of quasi-coherent sheaves. In this note we present a detailed proof of this result…
A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.
We solve a case of the Abelian Exponential-Algebraic Closedness Conjecture, a conjecture due to Bays and Kirby, building on work of Zilber, which predicts sufficient conditions for systems of equations involving algebraic operations and the…
We provide a broad class of counterexamples to a conjecture of L. de Branges concerning the superfluity of the continuity property in the axiomatic description of de Branges spaces.
A short proof of a conjecture of Kropholler is given. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, that gives…