Takeuti, Gaisi 19262017
Overview
Works:  70 works in 293 publications in 6 languages and 5,605 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Honoree, Editor 
Classifications:  QA9.54, 511.3 
Publication Timeline
.
Most widely held works by
Gaisi Takeuti
Memoirs of a proof theorist : Gödel and other logicians by
Gaisi Takeuti(
)
19 editions published in 2003 in English and held by 1,392 WorldCat member libraries worldwide
This volume is a translation of the book Gödel, written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the book comprises a memoir of K. Gödel, Takeuti's personal recollections, and his interpretation of Gödel's attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. Everything in the book is original, as the author adheres to his own experiences and interpretations. There is also an article on Hilbert's second problem as well as on the author's fundamental conjecture about second order logic
19 editions published in 2003 in English and held by 1,392 WorldCat member libraries worldwide
This volume is a translation of the book Gödel, written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the book comprises a memoir of K. Gödel, Takeuti's personal recollections, and his interpretation of Gödel's attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. Everything in the book is original, as the author adheres to his own experiences and interpretations. There is also an article on Hilbert's second problem as well as on the author's fundamental conjecture about second order logic
Introduction to axiomatic set theory by
Gaisi Takeuti(
Book
)
33 editions published between 1970 and 1982 in 3 languages and held by 992 WorldCat member libraries worldwide
In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are high lighted, and second, the student who wishes to master the subject is com pelled to develop the detail on his own. However, an instructor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text
33 editions published between 1970 and 1982 in 3 languages and held by 992 WorldCat member libraries worldwide
In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are high lighted, and second, the student who wishes to master the subject is com pelled to develop the detail on his own. However, an instructor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text
Proof theory by
Gaisi Takeuti(
Book
)
43 editions published between 1975 and 2013 in 5 languages and held by 927 WorldCat member libraries worldwide
"This comprehensive monograph is a cornerstone in the area of mathematical logic and related fields. Focusing on Gentzentype proof theory, the book presents a detailed overview of creative works by the author and other 20thcentury logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition"
43 editions published between 1975 and 2013 in 5 languages and held by 927 WorldCat member libraries worldwide
"This comprehensive monograph is a cornerstone in the area of mathematical logic and related fields. Focusing on Gentzentype proof theory, the book presents a detailed overview of creative works by the author and other 20thcentury logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition"
Two applications of logic to mathematics by
Gaisi Takeuti(
)
5 editions published in 1978 in English and held by 617 WorldCat member libraries worldwide
5 editions published in 1978 in English and held by 617 WorldCat member libraries worldwide
Axiomatic set theory by
Gaisi Takeuti(
Book
)
22 editions published between 1973 and 2013 in 3 languages and held by 540 WorldCat member libraries worldwide
This text deals with three basic techniques for constructing models of ZermeloFraenkel set theory: relative constructibility, Cohen's forcing, and ScottSolovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain fundamental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," SpringerVerlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite selfcontained
22 editions published between 1973 and 2013 in 3 languages and held by 540 WorldCat member libraries worldwide
This text deals with three basic techniques for constructing models of ZermeloFraenkel set theory: relative constructibility, Cohen's forcing, and ScottSolovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain fundamental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," SpringerVerlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite selfcontained
Logic Symposia, Hakone, 1979, 1980 : proceedings of conferences held in Hakone, Japan, March 2124, 1979 and February 47,
1980 by
G. H Müller(
Book
)
20 editions published between 1981 and 2006 in English and held by 511 WorldCat member libraries worldwide
20 editions published between 1981 and 2006 in English and held by 511 WorldCat member libraries worldwide
Two applications of logic to mathematics by
Gaisi Takeuti(
)
16 editions published between 1978 and 2016 in English and held by 144 WorldCat member libraries worldwide
Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott Solovay's Booleanvalued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that any arithmetical theorem proved in analytic number theory is a theorem in Peano's arithmetic. In doing so, the author applies Gentzen's cut elimination theorem. Although the results of Part One may be regarded as straightforward consequences of the spectral theorem in function analysis, the use of Boolean valued models makes explicit and precise analogies used by analysts to lift results from ordinary analysis to operators on a Hilbert space. Essentially expository in nature, Part Two yields a general method for showing that analytic proofs of theorems in number theory can be replaced by elementary proofs. Originally published in 1978. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
16 editions published between 1978 and 2016 in English and held by 144 WorldCat member libraries worldwide
Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott Solovay's Booleanvalued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that any arithmetical theorem proved in analytic number theory is a theorem in Peano's arithmetic. In doing so, the author applies Gentzen's cut elimination theorem. Although the results of Part One may be regarded as straightforward consequences of the spectral theorem in function analysis, the use of Boolean valued models makes explicit and precise analogies used by analysts to lift results from ordinary analysis to operators on a Hilbert space. Essentially expository in nature, Part Two yields a general method for showing that analytic proofs of theorems in number theory can be replaced by elementary proofs. Originally published in 1978. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
Logic Symposia Hakone 1979, 1980 : Proceedings of Conferences Held in Hakone, Japan March 2124, 1979 and February 47, 1980 by
Gert H Müller(
)
2 editions published in 1981 in English and held by 74 WorldCat member libraries worldwide
2 editions published in 1981 in English and held by 74 WorldCat member libraries worldwide
Formally selfreferential propositions for cut free classical analysis and related systems by
Georg Kreisel(
Book
)
2 editions published in 1974 in English and held by 49 WorldCat member libraries worldwide
2 editions published in 1974 in English and held by 49 WorldCat member libraries worldwide
Chokkan shugiteki shūgōron by
Gaisi Takeuti(
)
2 editions published in 1980 in Japanese and held by 48 WorldCat member libraries worldwide
2 editions published in 1980 in Japanese and held by 48 WorldCat member libraries worldwide
Sūgakuteki sekaikan : gendai sūgaku no shisō to tenbō by
Gaisi Takeuti(
)
5 editions published in 1982 in Japanese and held by 41 WorldCat member libraries worldwide
5 editions published in 1982 in Japanese and held by 41 WorldCat member libraries worldwide
Introduction to axiomatic set theory by
Gaisi Takeuti(
Book
)
15 editions published between 1970 and 2013 in 3 languages and held by 36 WorldCat member libraries worldwide
15 editions published between 1970 and 2013 in 3 languages and held by 36 WorldCat member libraries worldwide
Proof theory by
Gaisi Takeuti(
Book
)
3 editions published between 1975 and 1987 in English and held by 34 WorldCat member libraries worldwide
3 editions published between 1975 and 1987 in English and held by 34 WorldCat member libraries worldwide
Logic Symposia, Hakone, 1979, 1980 : proceedings of conferences held in Hakone, Japan, March 2124, 1979 and February 47,
1980 by Logic Symposia(
Book
)
3 editions published in 1981 in English and held by 29 WorldCat member libraries worldwide
3 editions published in 1981 in English and held by 29 WorldCat member libraries worldwide
Formally selfreferential propositions for cut free classical analysis and related system by
Georg Kreisel(
Book
)
5 editions published in 1974 in English and Undetermined and held by 23 WorldCat member libraries worldwide
5 editions published in 1974 in English and Undetermined and held by 23 WorldCat member libraries worldwide
Shūgō towa nanika : Hajimete manabu hito no tameni by
Gaisi Takeuti(
Book
)
7 editions published between 1976 and 2001 in Japanese and held by 14 WorldCat member libraries worldwide
7 editions published between 1976 and 2001 in Japanese and held by 14 WorldCat member libraries worldwide
Two applications of logic to mathematics by
Gaisi Takeuti(
Book
)
1 edition published in 1978 in English and held by 13 WorldCat member libraries worldwide
1 edition published in 1978 in English and held by 13 WorldCat member libraries worldwide
Arithmetic, proof theory, and computational complexity by
Peter Clote(
Book
)
1 edition published in 1993 in English and held by 10 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 10 WorldCat member libraries worldwide
Mugensho kaiseki to butsurigaku by
Gaisi Takeuti(
Book
)
5 editions published between 1985 and 2001 in Japanese and held by 7 WorldCat member libraries worldwide
5 editions published between 1985 and 2001 in Japanese and held by 7 WorldCat member libraries worldwide
Two applications of logic to mathematics by
Gaisi Takeuti(
Book
)
2 editions published in 1978 in Italian and English and held by 7 WorldCat member libraries worldwide
2 editions published in 1978 in Italian and English and held by 7 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Zaring, Wilson M.
 Gödel, Kurt
 Tugué, T. (Tosiyuki) 1926 Editor
 Müller, G. H. (Gert Heinz) 1923 Author Editor
 Kreisel, Georg Author
 Müller, Gert Author
 Yasugi, Mariko Other Translator
 Passell, Nicholas Other Translator
 Clote, Peter Editor
 Krajíček, Jan Editor
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Alternative Names
Gaishi, Takeuchi 1926
Gaisi, Takeuti 1926
Gaisi Takeuti Japanese mathematician
Gaisi Takeuti japanischer Philosoph und Mathematiker
Gaisi Takeuti Japans wiskundige (19262017)
Gaisi Takeuti matemático japonés
Gaisi Takeuti mathématicien japonais
Takeuchi, Gaishi
Takeuchi, Gaishi 1926
Takeuchi, Gaishi 19262017
Takeuchi, Gaisi 1926
Takeuti, G.
Takeuti, G. 19262017
Takeuti, Gaishi 1926
Takeuti, Gaisi
Takeuti Gaisi 1926....
Такеути, Г..
다케우치 가이시
タケウチ, ガイシ
タケウチ, ガイシ 1926
タケウチ, ガイシ, 19262017
竹内外史
竹内外史 1926
竹内外史, 19262017
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