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# Proof Theory The First Step into Impredicativity by Wolfram Pohlers

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Published by Springer-Verlag Berlin Heidelberg in Berlin, Heidelberg .
Written in English

### Subjects:

• Symbolic and mathematical Logic

## Book details:

Edition Notes

The Physical Object ID Numbers Statement by Wolfram Pohlers Series Universitext Contributions SpringerLink (Online service) Format [electronic resource] : Open Library OL25539242M ISBN 10 9783540693185, 9783540693192

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Books on logic, proof theory and set theory? Ask Question Asked 6 years, 9 months ago. Prior's book has sections on propositional calculus, quantification theory, the Aristotelian syllogistic, traditional logic, modal logic, three-valued logic, and the logic of extension. Browse other questions tagged reference-request logic set-theory. Proof theory was created early in the 20th century by David Hilbert to prove the consistency of the ordinary methods of reasoning used in mathematics| in arithmetic (number theory), analysis and set theory. Already in his famous \Mathematical problems" of . Takeuti's Proof Theory (2nd ed.) has recently been republished as a Dover book, so it's cheap. Not exactly easy going though. I was recently bemoaning the lack of approachable proof theory textbooks to a colleague who's from that world, but unfortunately he couldn't offer any better suggestions for introductory books. Contents Preface vii Introduction viii I Fundamentals 1. Sets 3 IntroductiontoSets 3 TheCartesianProduct 8 Subsets 11 PowerSets 14 Union,Intersection,Diﬀerence

Proof theory is a major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system.   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 Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other /5(5). "The book is addressed primarily to students of mathematical logic interested in the basics of proof theory, and it can be used both for introductory and advanced courses in proof theory. this book may be recommended to a larger circle of readers interested in proof theory." (Branislav Boricic, Zentrablatt MATH, Vol. , )Brand: Springer-Verlag Berlin Heidelberg. This comprehensive monograph is a cornerstone in the area of mathematical logic and related fields. Focusing on Gentzen-type proof theory, the book presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. edition.

The book starts with the basics of set theory, logic and truth tables, and counting. Then, the book moves on to standard proof techniques: direct proof, proof by contrapositive and contradiction, proving existence and uniqueness, constructive proof, proof by induction, and others/5(6). This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook see the Mathematical Association of America Math DL review (of the 1st edition) and the Amazon reviews. An adoptions li st is here. details. Some book in proof theory, such as [Gir], may be useful afterwards to complete the information on those points which are lacking. The notes would never have reached the standard of a book without the interest taken in translating (and in many cases reworking) them by Yves Lafont and Paul Taylor. Book article: Samuel R. Buss. "An Introduction to Proof Theory" in Handbook of Proof Theory, edited by S. R. Buss. Elsevier, Amsterdam, , pp Download article: postscript or PDF. Table of contents: This is an introduction to proof complexity. Proof theory and Propositional Logic. Frege proof systems. The propositional sequent calculus.