Related papers: A Direct Proof of the Theorem on Formal Functions
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
We define the notion of sheaf in the context of doctrines. We prove the associate sheaf functor theorem. We show that grothendieck toposes and toposes obtained by the tripos to topos construction are instances of categories of sheaves for a…
In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…
Choreographic programming is a paradigm for writing coordination plans for distributed systems from a global point of view, from which correct-by-construction decentralised implementations can be generated automatically. Theory of…
We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…
We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is…
`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program…
We define a Dieudonn\'e module as the module of Dieudonn\'e elements, and set up Dieudonn\'e module theory in a simple way. Under this formulation we give explicit formulae for the duality and the corresponding differential operators.
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction…
Thanks to Hrushovski-Loeser's work on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom-Sebastiani theorem in the case of regular functions. Moreover, slightly extending of Hrushovski-Loeser's construction adjusted…
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…
We prove a representability theorem for moduli functors of framed torsion-free sheaves on nonsingular complex projective surfaces, using formal geometry along a curve in the surface. This has as a consequence that a certain restriction…
This paper presents a novel direct elementary proof for Fermat's Last Theorem. We use algebra, modular math, and binomial series to develop inherent mathematical relationships hidden within Fermat's Last Theorem. With these derived…
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…
Boolos's proof of incompleteness is extended straightforwardly to yield simple ``diagonalization-free'' proofs of some classical limitative theorems of logic.
The purpose of this article is threefold: Firstly, we propose some enhancements to the existing definition of 6-functor formalisms. Secondly, we systematically study the category of kernels, which is a certain 2-category attached to every…
Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.
This report presents a formalization of May's theorem in the proof assistant Coq. It describes how the theorem statement is first translated into Coq definitions, and how it is subsequently proved. Various aspects of the proof and related…