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Proof Theory
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The article was published on 1975-01-01 and is currently open access. It has received 770 citations till now. The article focuses on the topics: Proof theory & Gentzen's consistency proof.read more
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Journal ArticleDOI
Systems of explicit mathematics with non-constructive μ-operator. Part I
Solomon Feferman,Gerhard Jäger +1 more
TL;DR: The principal results then state: (i) BON(μ) plus set induction is proof-theoretically equivalent to Peano arithmetic PA; (ii) Bon( μ) plus formula induction isProof- theoretical equivalent to the system (Π0∞-CA)
Journal ArticleDOI
A uniform semantic proof for cut-elimination and completeness of various first and higher order logics
TL;DR: A natural generalization of Girard's (first order) phase semantics of linear logic to intuitionistic and higher-order phase semantics is presented, which allows for a uniform semantic proof of the cut-elimination theorem and a higher order phase-semantic completeness theorem for various different logical systems at the same time.
Journal ArticleDOI
Universal algebra in higher types
TL;DR: Basic results include: existence theorems for free and initial higher type algebras, a complete higher type equational calculus, and characterisation theorem for higher type Equational and Horn classes.
Book ChapterDOI
Systems of Deduction
TL;DR: Formal calculi of deduction have proved useful in logic and in the foundations of mathematics, as well as in metamathematics, and certain versions of formal calculi have been used in attempts to formulate philosophical insights into the nature of reasoning.
Book ChapterDOI
Hypersequent and the Proof Theory of Intuitionistic Fuzzy Logic
Matthias Baaz,Richard Zach +1 more
TL;DR: In this article, it is shown that the first-order Godel logic is axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known.