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Original: $19.99
-65%Proof Theory—
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$7.00The Story
Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
Reprint of the North-Holland, Amsterdam, 1987 second revised edition.
gentzen type theory, essential math book, undergraduate math, graduate math, applications of proof theory, mathematical logic, monograph, first order systems, predicate calculus, cut elimination theorem, theory of natural numbers, godel, incompleteness theorem, consistency proof, second order, finite systems, simple type theory, infinitary logic, consistency problems in mathematics, consistency proof applications, auxiliary formulas, comprehensive monographs, math theoryDescription
Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
Reprint of the North-Holland, Amsterdam, 1987 second revised edition.
gentzen type theory, essential math book, undergraduate math, graduate math, applications of proof theory, mathematical logic, monograph, first order systems, predicate calculus, cut elimination theorem, theory of natural numbers, godel, incompleteness theorem, consistency proof, second order, finite systems, simple type theory, infinitary logic, consistency problems in mathematics, consistency proof applications, auxiliary formulas, comprehensive monographs, math theory
