skip to content
Proof theory Preview this item
ClosePreview this item
Checking...

Proof theory

Author: Gaisi Takeuti
Publisher: Mineola, New York : Dover Publications, 2013.
Series: Dover books on mathematics.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Database:WorldCat
Summary:
"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. 1975 edition"--
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Takeuti, Gaisi, 1926-
Proof theory.
(DLC) 2012030734
(OCoLC)792881195
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gaisi Takeuti
ISBN: 9780486320670 0486320677
OCLC Number: 867772409
Description: 1 online resource (x, 490 pages).
Contents: Cover; Title Page; Copyright Page; Preface; Preface to the Second Edition; Contents; Introduction; Part I. First Order Systems; Chapter 1. First Order Predicate Calculus; 1. Formalization of statements; 2. Formal proofs and related concepts; 3. A formulation of intuitionistic predicate calculus; 4. Axiom systems; 5. The cut-elimination theorem; 6. Some consequences of the cut-elimination theorem; 7. The predicate calculus with equality; 8. The completeness theorem; Chapter 2. Peano Arithmetic; 9. A formulation of Peano arithmetic; 10. The incompleteness theorem. 11. A discussion of ordinals from a finitist standpoint12. A consistency proof of PA; 13. Provable well-orderings; 14. An additional topic; Part II. Second Order and Finite Order Systems; Chapter 3. Second Order Systems and Simple Type Theory; 15. Second order predicate calculus; 16. Some systems of second order predicate calculus; 17. The theory of relativization; 18. Truth definition for first order arithmetic; 19. The interpretation of a system of second order arithmetic; 20. Simple type theory; 21. The cut-elimination theorem for simple type theory; Chapter 4. Infinitary Logic. 22. Infinitary logic with homogeneous quantifiers23. Determinate logic; 24. A general theory of heterogeneous quantifiers; Part III. Consistency Problems; Chapter 5. Consistency Proofs; 25. Introduction; 26. Ordinal diagrams; 27. A consistency proof of second order arithmetic with the [pi]11-comprehension axiom; 28. A consistency proof for a system with inductive definitions; Chapter 6. Some Applications of Consistency Proofs; 29. Provable well-orderings; 30. The [pi]11-comprehension axiom and the [omega]-rule; 31. Reflection principles; Postscript; Appendix; Proof Theory by Georg Kreisel. Contributions of the Schütte School by Wolfram PohlersSubsystems of Z2 and Reverse Matfiematics by Stephen G. Simpson; Proof Theory: A Personal Report by Solomon Feferman; Index.
Series Title: Dover books on mathematics.
Responsibility: Gaisi Takeuti, Professor Emeritus of Mathematics, the University of Illinois at Urbana-Champaign.

Abstract:

"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. 1975 edition"--

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/867772409> # Proof theory
    a schema:CreativeWork, schema:Book, schema:MediaObject ;
   library:oclcnum "867772409" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/2406532#Topic/calculus> ; # Calculus
   schema:about <http://experiment.worldcat.org/entity/work/data/2406532#Topic/mathematics_logic> ; # MATHEMATICS--Logic
   schema:about <http://experiment.worldcat.org/entity/work/data/2406532#Topic/mathematics> ; # Mathematics
   schema:about <http://dewey.info/class/511.36/e23/> ;
   schema:about <http://id.worldcat.org/fast/1078942> ; # Proof theory
   schema:bookEdition "Second edition." ;
   schema:bookFormat schema:EBook ;
   schema:creator <http://viaf.org/viaf/64133112> ; # Gaisi Takeuti
   schema:datePublished "2013" ;
   schema:description ""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. 1975 edition"--"@en ;
   schema:description "Cover; Title Page; Copyright Page; Preface; Preface to the Second Edition; Contents; Introduction; Part I. First Order Systems; Chapter 1. First Order Predicate Calculus; 1. Formalization of statements; 2. Formal proofs and related concepts; 3. A formulation of intuitionistic predicate calculus; 4. Axiom systems; 5. The cut-elimination theorem; 6. Some consequences of the cut-elimination theorem; 7. The predicate calculus with equality; 8. The completeness theorem; Chapter 2. Peano Arithmetic; 9. A formulation of Peano arithmetic; 10. The incompleteness theorem."@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/2406532> ;
   schema:genre "Electronic books"@en ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/2406532#Series/dover_books_on_mathematics> ; # Dover books on mathematics.
   schema:isSimilarTo <http://www.worldcat.org/oclc/792881195> ;
   schema:name "Proof theory"@en ;
   schema:productID "867772409" ;
   schema:url <http://www.freading.com/ebooks/details/r:download/ZnJlYWQ6OTc4MDQ4NjMyMDY3MDpl> ;
   schema:url <http://public.eblib.com/choice/publicfullrecord.aspx?p=1893182> ;
   schema:url <http://ebookcentral.proquest.com/lib/ucm/detail.action?docID=1893182> ;
   schema:workExample <http://worldcat.org/isbn/9780486320670> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/867772409> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/2406532#Series/dover_books_on_mathematics> # Dover books on mathematics.
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/867772409> ; # Proof theory
   schema:name "Dover books on mathematics." ;
   schema:name "Dover Books on Mathematics" ;
    .

<http://experiment.worldcat.org/entity/work/data/2406532#Topic/mathematics_logic> # MATHEMATICS--Logic
    a schema:Intangible ;
   schema:name "MATHEMATICS--Logic"@en ;
    .

<http://id.worldcat.org/fast/1078942> # Proof theory
    a schema:Intangible ;
   schema:name "Proof theory"@en ;
    .

<http://viaf.org/viaf/64133112> # Gaisi Takeuti
    a schema:Person ;
   schema:birthDate "1926" ;
   schema:deathDate "2017" ;
   schema:familyName "Takeuti" ;
   schema:givenName "Gaisi" ;
   schema:name "Gaisi Takeuti" ;
    .

<http://worldcat.org/isbn/9780486320670>
    a schema:ProductModel ;
   schema:isbn "0486320677" ;
   schema:isbn "9780486320670" ;
    .

<http://www.worldcat.org/oclc/792881195>
    a schema:CreativeWork ;
   rdfs:label "Proof theory." ;
   schema:description "Print version:" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/867772409> ; # Proof theory
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.