333 research outputs found

    Constructive Theory of Banach algebras

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    We present a way to organize a constructive development of the theory of Banach algebras, inspired by works of Cohen, de Bruijn and Bishop. We illustrate this by giving elementary proofs of Wiener's result on the inverse of Fourier series and Wiener's Tauberian Theorem, in a sequel to this paper we show how this can be used in a localic, or point-free, description of the spectrum of a Banach algebra

    ProofPeer - A Cloud-based Interactive Theorem Proving System

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    ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented as a solution to the problem of sharing proof state among the users of ProofPeer. Chronicles are introduced as a way to organize and version contexts

    A theory and its metatheory in FS 0

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    Feferman has proposed FS0, a theory of finitary inductive systems, as a framework theory suitable for various purposes, including reasoning both in and about encoded theories. I look here at how practical FS0 really is. I formalise of a sequent calculus presentation of classical propositional logic in FS0 and show this can be used for work in both the theory and the metatheory. the latter is illustrated with a discussion of a proof of Gentzen's Hauptsatz
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