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Description
Algebra of Proofs deals with algebraic properties of the proof theory of intuitionist first-order logic in a categorical setting. The presentation is based on the confluence of ideas and techniques from proof theory, category theory, and combinatory logic. The conceptual basis for the text is the Lindenbaum-Tarski algebras of formulas taken as categories. The formal proofs of the associated deductive systems determine structured categories as their canonical algebras (which are of the same type as the Lindenbaum-Tarski algebras of the formulas of underlying languages). Gentzen's theorem, which asserts that provable formulas code their own proofs, links the algebras of formulas and the corresponding algebras of formal proofs. The book utilizes the Gentzen's theorem and the reducibility relations with the Church-Rosser property as syntactic tools. The text explains two main types of theories with varying linguistic complexity and deductive strength: the monoidal type and the Cartesian type. It also shows that quantifiers fit smoothly into the calculus of adjoints and describe the topos-theoretical setting in which the proof theory of intuitionist first-order logic possesses a natural semantics. The text can benefit mathematicians, students, or professors of algebra and advanced mathematics.
Pages
310 pages
Collection
n.c
Parution
2016-06-03
Marque
North Holland
EAN papier
9781483230726
EAN PDF SANS DRM
9781483275420
Informations sur l'ebook
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
57,97 €

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