相关论文: Remarks on Barr's theorem: Proofs in geometric the…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

We prove Barth-type connectedness results for low-codimension smooth subvarieties with good numerical properties inside certain "easy" ambient spaces (such as homogeneous varieties, or spherical varieties). The argument employs some basics…

We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory.…

A theorem of Ku\v{c}era states that given a Martin-L\"of random infinite binary sequence {\omega} and an effectively open set A of measure less than 1, some tail of {\omega} is not in A. We first prove several results in the same spirit and…

Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform…

Using Butz and Moerdijk's topological groupoid representation of a topos with enough points, a `syntax-semantics' duality for geometric theories is constructed. The emphasis is on a logical presentation, starting with a description of the…

This paper attempts to provide an analogue of the Novikov conjecture for algebraic (or K\"{a}hler) manifolds. Inter alia, we prove a conjecture of Rosenberg's on the birational invariance of higher Todd genera. We argue that in the…

Tennenbaum's theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive type theory as a framework to revisit,…

These notes cover the contents of three survey lectures held at the ICTP Trieste Summer school on High dimensional manifold theory 2001. They introduce techniques coming from the theory of operator algebras. We will focus on the basic…

In this paper, we show how geometry plays in the study of the Furstenberg conjecture (refer to~\cite{F}). Let $p>1$ and $q>1$ be two relative prime positive integers. We prove that a non-atomic $p$- and $q$-invariant measure having balanced…

The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues's Theorem, harmonic conjugates, projectivities, involutions, conics, Pascal's Theorem,…

Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the…

We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…

This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae…

This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group $G$ is…

Menger conjectured that subsets of R with the Menger property must be ${\sigma}$-compact. While this is false when there is no restriction on the subsets of R, for projective subsets it is known to follow from the Axiom of Projective…

One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…

This paper introduces a model theory for resolution on Higher Order Hereditarily Harrop formulae (HOHH), the logic underlying the Lambda-Prolog programming language, and proves soundness and completeness of resolution. The semantics and the…

Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that…

Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is $(r+1)$-vertex connected, $1 \leq r \leq n-2$, then there exists a configuration $p$ in general position in $R^r$ such that the bar framework $(G,p)$ is universally…