Gaisi Takeuti

Q: What Schools Are Affiliated With Gaisi Takeuti

Gaisi Takeuti is affiliated with the following schools: Tokyo University of Education, University of Tokyo, Princeton University, University of Illinois Urbana-Champaign

Gaisi Takeuti's AcademicInfluence.com Rankings

Gaisi Takeuti

Mathematics

#698

World Rank

#1279

Historical Rank

Measure Theory

#1091

World Rank

#1404

Historical Rank

mathematics Degrees

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Mathematics

Gaisi Takeuti's Degrees

PhD Mathematics University of Tokyo

Why Is Gaisi Takeuti Influential?

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According to Wikipedia, Gaisi Takeuti was a Japanese mathematician, known for his work in proof theory. After graduating from Tokyo University, he went to Princeton to study under Kurt Gödel. He later became a professor at the University of Illinois at Urbana–Champaign. Takeuti was president of the Kurt Gödel Society, having worked on the book Memoirs of a Proof Theorist: Godel and Other Logicians. His goal was to prove the consistency of the real numbers. To this end, Takeuti's conjecture speculates that a sequent formalisation of second-order logic has cut-elimination. He is also known for his work on ordinal diagrams with Akiko Kino.

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Gaisi Takeuti's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Proof Theory (1975) (354)
Intuitionistic fuzzy logic and intuitionistic fuzzy set theory (1984) (269)
Bounded Arithmetic and the Polynomial Hierarchy (1991) (170)
Two Applications of Logic to Mathematics (1978) (123)
On a generalized logic calculus (1953) (94)
Globalization of intui tionistic set theory (1987) (90)
Quantum Set Theory (1981) (90)
Introduction to axiomatic set theory (1971) (77)
Consistency Proofs of Subsystems of Classical Analysis (1967) (74)
Fuzzy logic and fuzzy set theory (1992) (71)
First Order Bounded Arithmetic and Small Boolean Circuit Complexity Classes (1995) (66)
Bounded Arithmetic for NC, ALogTIME, L and NL (1992) (56)
Formally self-referential propositions for cut free classical analysis and related systems (1974) (48)
Axiomatic Set Theory (1973) (46)
On the fundamental conjecture of GLC, VI (1955) (44)
Von Neumann algebras and Boolean valued analysis (1983) (44)
On the recursive functions of ordinal numbers (1960) (39)
C*-algebras and Boolean valued analysis (1983) (33)
A transfer principle in harmonic analysis (1979) (31)
Ordinal Diagrams II. (1960) (28)
Bounded arithmetic and truth definition (1988) (26)
A formalization of the theory of ordinal numbers (1965) (25)
First order topology (1977) (25)
On induction-free provability (1992) (21)
Remark on my paper: On Skolem's theorem. (1957) (21)
The ordinals of the systems of second order arithmetic with the provably Δ 2 1 -comprehension axiom and with the Δ 2 1 -comprehension axiom respectively (1973) (19)
Construction of the set theory from the theory of ordinal numbers (1954) (18)
A formal system of first-order predicate calculus with infinitely long expressions (1961) (18)
Heyting valued universes of intuitionistic set theory (1981) (17)
On Bounded ∑ 1 1 Polynomial Induction (1990) (16)
On the theory of quasi-ordinal diagrams (1985) (16)
Exponential Time and Bounded Arithmetic (1986) (16)
On the theory of ordinal numbers (1957) (14)
On predicates with constructive infinitely long expressions (1963) (13)
Boolean valued analysis (1979) (13)
On the inductive definition with quantifiers of second order (1961) (11)
Formally Self-Referential Propositions for Cut Free Analysis and Related Systems (1985) (10)
The Universe of Set Theory (1969) (10)
Some Relations among Systems for Bounded Arithmetic (1990) (10)
On hierarchies of predicates of ordinal numbers (1962) (10)
Boolean completion and m-convergence (1982) (9)
A Determinate Logic (1970) (9)
Gödel sentences of bounded arithmetic (2000) (9)
Errata to ‘On a Generalized Logic Calculus’ (1954) (8)
Boolean simple groups and boolean simple rings (1988) (8)
Provably Total Functions in Bounded Arithmetic Theories Ri 3 , U i 2 and V i 2 (2002) (8)
Forcing on bounded arithmetic II (1998) (8)
A Relativization of Axioms of Strong Infinity to ω1 (1970) (8)
On the theory of ordinal numbers, II. (1957) (7)
Transcendence of cardinals (1965) (7)
On the Formal Theory of the Ordinal Diagrams (1958) (7)
Grzegorcyk's hierarchy and IepΣ1 (1994) (6)
A second order version of S 2 i and U 2 1 (1991) (6)
Global intuitionistic analysis (1986) (6)
RSUV isomorphisms for TACi, TNCi and TLS (1995) (6)
A metamathematical theorem on functions. (1956) (6)
Separations of Theories in Weak Bounded Arithmetic (1995) (5)
Fundamental sequences of ordinal diagrams (1976) (5)
Two interpolation theorems for a predicate calculus (1971) (5)
Proof theory and set theory (1985) (5)
Logic Symposia Hakone 1979, 1980 (1981) (5)
Frege proof system and TNC° (1994) (5)
An accessibility proof of ordinal diagrams (1981) (5)
Remark on the fundamental conjecture of $GLC$ . (1958) (5)
Axioms of infinity of set theory (1961) (5)
A metamathematical theorem on the theory of ordinal numbers (1952) (4)
Consistency proofs and ordinals (1975) (4)
An example on the fundamental conjecture of $GLC$ . (1960) (4)
Review: Kurt Schutte, Syntactical and Semantical Properties of Simple Type Theory (1967) (4)
On Skolem's theorem (1957) (4)
Remarks on Cantor's Absolute. II (1961) (3)
Meetings of the Association for Symbolic Logic, U.S.-Japan Logic Seminar, Tokyo 1969 (1971) (3)
Logic and Set Theory (1981) (3)
Incompleteness Theorems and S i 2 versus S i+1 2@@@Godel Sentences of Bounded Arithmetic (2002) (3)
Meeting of the Association for Symbolic Logic, Chicago, 1977 (1976) (3)
Gödel numbers of product spaces (1978) (2)
The Π 1 1 -comprehension schema and ω-rules (1968) (2)
Introduction to Axiomatic Set Theory.@@@Axiomatic Theory of Sets and Classes. (1972) (2)
A note on predicates of ordinal numbers (1962) (2)
Remarks on Cantor's Absolute (1961) (2)
A Second Order Version of Si2 and U12 (1991) (2)
On the fundamental conjecture of $GLC$ V. (2009) (2)
On the fundamental conjecture of $GLC$ V. (2009) (2)
Frege Proof System and TNC$^\circ$ (1998) (1)
On the Decomposition of Boolean Polynomials (1977) (1)
Functions and Relations (1971) (1)
The critical number of a variable in a function (1994) (1)
Reflection Principles of Subsystems of Analysis: Dedicated to Professor S. Iyanaga for his 60th birthday (1968) (1)
Weak Distributive Laws (1973) (1)
Work of Paul Bernays and Kurt Gödel (1982) (1)
Incompleteness theorems and Si2 versus Si2 (2016) (1)
Chapter 1. Real Analysis (2015) (0)
Gödel sentences and bounded arithmetic (2009) (0)
Remarks on the truth deﬁnition (2009) (0)
Construction of Ramified Real Numbers (1956) (0)
Foundations of Mathematics (1959) (0)
Incompleteness theoremand its frontier (2016) (0)
The Axiom of Choice, the Generalized Continuum Hypothesis and Cardinal Arithmetic (1971) (0)
The Independence of V = L and the CH (1973) (0)
Boolean Algebras That Are Not Sets (1973) (0)
Boolean-Valued Set Theory (1973) (0)
Model Theoretic Consequences of the Distributive Laws (1973) (0)
Relational Closure and the Rank Function (1982) (0)
Cardinals in V(B) (1973) (0)
A generalization of König's lemma (1963) (0)
Boolean-Valued Relative Constructibility (1973) (0)
Grzegorcyk's Hierarchy and Iep Sigma1 (1994) (0)
Chapter 2. Boolean Valued Analysis Using Measure Algebras (2015) (0)
The Independence of the AC (1973) (0)
The Maximum Principle (1973) (0)
Boolean σ-Algebras (1973) (0)
Review: Setsuya Seki, Introduction to set Theory (1959) (0)
Cofinality, the Generalized Continuum Hypothesis, and Cardinal Arithmetic (1982) (0)
Kurt Gödel and the Foundations of Mathematics: Foreword (2011) (0)
Remarks on the truth definition (1961) (0)
The Axiom of Choice and Cardinal Numbers (1982) (0)
On the inductive deﬁnition with quantiﬁers of second order (2009) (0)
Language and Logic (1971) (0)
Chapter 2. Complex Analysis (2015) (0)
Relative Constructibility and Ramified Languages (1973) (0)
Remarks on Cantor's Absolute,pt.2. (1961) (0)
Review: Setsuya Seki, Report of a Symposium (1960) (0)
Applications of Silver Machines (1982) (0)
Seki Setsuya. Symposium hôkokusyû (Report of a symposium). Kisoron Bunkakai Nihon Sûgakukai, Tokyo 1959, 47 pp. (1960) (0)
Axioms of inﬁnity of set theory (2009) (0)
Partial Order Structures and Topological Spaces (1973) (0)
On the weak definability in set theory. (1962) (0)
The Gödel Model (1971) (0)
Another Interpretation of V(B) (1973) (0)
The Fundamental Operations (1971) (0)
Frege Proof System and TNCdegree (1998) (0)
Independence Results Using the Models V(B) (1973) (0)
The Completion of a Boolean Algebra (1973) (0)
The Arithmetization of Model Theory (1971) (0)
Languages, Structures, and Models (1971) (0)
An Elementary Embedding of V [ F 0 ] in V (B) (1973) (0)
Boolean-Valued Structures (1973) (0)
Chapter 1. Boolean Valued Analysis Using Projection Algebras (2015) (0)
A Proof of Marczewski’s Theorem (1973) (0)
Review: Setsuya Seki, Foundations of Mathematics (1959) (0)
Logic Symposia, Hakone, 1979, 1980: Proceedings of Conferences Held in Hakone, Japan, March 21-24, 1979 and February 4-7, 1980 (1981) (0)
The Elementary Properties of Classes (1971) (0)
Introduction to Forcing (1982) (0)

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What Schools Are Affiliated With Gaisi Takeuti?

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