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“…This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. …”
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“…This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. …”
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“…The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. …”
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“…This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. …”
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“…Kanger's dissertation Provability in Logic, 1957, contained significant results in proof theory as well as the first fully worked out model-theoretic interpretation of quantified modal logic. …”
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“…Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculus to prove a wide range of metatheoretical results. …”
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“…This major graduate-level text provides a detailed, self-contained coverage of proof theory.…”
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“…This book illustrates linear logic in the application of proof theory to computer science.…”
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“…Presents a new way of applying the methods of proof theory to axiomatic theories and systems of philosophical logic.…”
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“…This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. …”
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“…Crucially, in both cases, the proof involves a detour through ordinal analyses of infinitary systems of intuitionistic set theory, i.e. advanced techniques from proof theory. This article is part of the theme issue ‘Modern perspectives in Proof Theory’.…”
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“…In the first part we introduce and discuss the main philosophical ideas related to proof theory, and we try to identify criteria for distinguishing good sequent calculi. …”
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“…This article is part of the theme issue ‘Modern perspectives in Proof Theory’.…”
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“…Minimax strategies also generalize to the new class of games, and are computed by the Berardi–Bezem–Coquand functional, studied in proof theory as an interpretation of the axiom of countable choice.…”
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“…The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.…”
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“…After these successes, Gentzen dedicated the rest of his short life to the main problem of Hilbert's proof theory, the question of the consistency of analysis. …”
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“…This collection of papers celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his  seminal  research. …”
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“…The power and elegance of natural deduction is demonstrated best in the part of proof theory called `cut-elimination' or `normalization'. …”
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“…The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. …”
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