WorldCat Identities

Takeuti, Gaisi 1926-2017

Overview
Works: 63 works in 279 publications in 6 languages and 5,406 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Honoree, Editor
Publication Timeline
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Most widely held works about Gaisi Takeuti
 
Most widely held works by Gaisi Takeuti
Memoirs of a proof theorist : Gödel and other logicians by Gaisi Takeuti( )

18 editions published in 2003 in English and held by 1,370 WorldCat member libraries worldwide

This volume is a translation of the book "Godel", written in Japanese by Gaisi Takeuti, a distinguished proof theorist. The core of the text is a memoir of K. Godel, Takeuti's personal recollections, and his interpretation of Godel's comprises attitudes towards mathematical logic. It also contains Takeuti's recollection of association with some other famous logicians. 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
Proof theory by Gaisi Takeuti( Book )

46 editions published between 1975 and 2013 in 5 languages and held by 947 WorldCat member libraries worldwide

"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"--
Introduction to axiomatic set theory by Gaisi Takeuti( Book )

28 editions published between 1970 and 1982 in 3 languages and held by 913 WorldCat member libraries worldwide

In 1963, the first author introduced a course in set theory at the Uni­ versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con­ tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the 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 highlighted, and second, the student who wishes to master the sub­ ject is compelled to develop the details on his own. However, an in­ structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. For our slow development we claim the following advantages. The text is one from which a student can learn with little supervision and instruction. This enables the instructor to use class time for the presentation of alternative developments and supplementary material
Logic Symposia, Hakone, 1979, 1980 : proceedings of conferences held in Hakone, Japan, March 21-24, 1979 and February 4-7, 1980 by Logic Symposium. <1979 - 1980>( Book )

25 editions published between 1981 and 2006 in English and Undetermined and held by 593 WorldCat member libraries worldwide

Axiomatic set theory by Gaisi Takeuti( Book )

23 editions published between 1973 and 2013 in 3 languages and held by 531 WorldCat member libraries worldwide

This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay'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 funda­ mental 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," Springer-Verlag, 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 self-contained
Two applications of logic to mathematics by Gaisi Takeuti( Book )

5 editions published in 1978 in English and held by 527 WorldCat member libraries worldwide

Two Applications of Logic to Mathematics by Gaisi Takeuti( )

1 edition published in 2015 in English and held by 99 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 Boolean-valued 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 print-on-demand technology to again make available previously out-of-print 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
Introduction to Axiomatic Set Theory by Gaisi Takeuti( )

1 edition published in 1982 in English and held by 51 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
Formally self-referential propositions for cut free classical analysis and related systems by Georg Kreisel( Book )

2 editions published in 1974 in English and held by 50 WorldCat member libraries worldwide

Chokkan shugiteki shūgōron by Gaisi Takeuti( )

2 editions published in 1980 in Japanese and held by 46 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 39 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 34 WorldCat member libraries worldwide

Two applications of logic to mathematics by Gaisi Takeuti( Book )

6 editions published in 1978 in English and held by 29 WorldCat member libraries worldwide

Formally self-referential 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 22 WorldCat member libraries worldwide

Two applications of logic to mathematics by Gaisi Takeuti( Book )

7 editions published between 1978 and 2016 in English and held by 16 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

Two applications of logic to mathematics by Gaisi Takeuti( Book )

1 edition published in 1978 in English and held by 12 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

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

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

 
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Memoirs of a proof theorist : Gödel and other logicians
Covers
Logic Symposia, Hakone, 1979, 1980 : proceedings of conferences held in Hakone, Japan, March 21-24, 1979 and February 4-7, 1980Arithmetic, proof theory, and computational complexity
Alternative Names
Gaishi, Takeuchi 1926-

Gaisi, Takeuti 1926-

Gaisi Takeuti Japanese mathematician

Gaisi Takeuti matemático japonés

Gaisi Takeuti mathématicien japonais

Takeuchi, Gaishi

Takeuchi, Gaishi 1926-

Takeuchi, Gaishi 1926-2017

Takeuchi, Gaisi 1926-

Takeuti, G.

Takeuti, G. 1926-2017

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, 1926-2017

竹内外史

竹内外史 1926-

竹内外史, 1926-2017

Languages
English (167)

Japanese (19)

Russian (7)

Italian (4)

German (1)

Dutch (1)