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  1.  88
    Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set Theory.Gaisi Takeuti & Satoko Titani - 1984 - Journal of Symbolic Logic 49 (3):851-866.
  2.  16
    Bounded Arithmetic and the Polynomial Hierarchy.Jan Krajíček, Pavel Pudlák & Gaisi Takeuti - 1991 - Annals of Pure and Applied Logic 52 (1-2):143-153.
    T i 2 = S i +1 2 implies ∑ p i +1 ⊆ Δ p i +1 ⧸poly. S 2 and IΔ 0 ƒ are not finitely axiomatizable. The main tool is a Herbrand-type witnessing theorem for ∃∀∃ П b i -formulas provable in T i 2 where the witnessing functions are □ p i +1.
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  3.  11
    Fuzzy Logic and Fuzzy Set Theory.Gaisi Takeuti & Satoko Titani - 1992 - Archive for Mathematical Logic 32 (1):1-32.
  4.  10
    Globalization of Intui Tionistic Set Theory.Gaisi Takeuti & Satoko Titani - 1987 - Annals of Pure and Applied Logic 33 (2):195-211.
  5.  92
    Proof Theory and Set Theory.Gaisi Takeuti - 1985 - Synthese 62 (2):255 - 263.
    The foundations of mathematics are divided into proof theory and set theory. Proof theory tries to justify the world of infinite mind from the standpoint of finite mind. Set theory tries to know more and more of the world of the infinite mind. The development of two subjects are discussed including a new proof of the accessibility of ordinal diagrams. Finally the world of large cardinals appears when we go slightly beyond girard's categorical approach to proof theory.
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  6.  7
    Bounded Arithmetic and Truth Definition.Gaisi Takeuti - 1988 - Annals of Pure and Applied Logic 39 (1):75-104.
  7.  8
    On a Generalized Logic Calculus.Gaisi Takeuti - 1957 - Journal of Symbolic Logic 22 (4):351-352.
  8.  36
    A Formalization of the Theory of Ordinal Numbers.Gaisi Takeuti - 1965 - Journal of Symbolic Logic 30 (3):295-317.
  9.  21
    S 3 I andV 2 I (BD).Gaisi Takeuti - 1990 - Archive for Mathematical Logic 29 (3):149-169.
    No categories
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  10. Boolean Simple Groups and Boolean Simple Rings.Gaisi Takeuti - 1988 - Journal of Symbolic Logic 53 (1):160-173.
  11. Meetings of the Association for Symbolic Logic.Gaisi Takeuti - 1971 - Journal of Symbolic Logic 36 (2):357-384.
  12.  21
    Forcing on Bounded Arithmetic II.Gaisi Takeuti & Masahiro Yasumoto - 1998 - Journal of Symbolic Logic 63 (3):860-868.
  13.  9
    Introduction to Axiomatic Set Theory.Gaisi Takeuti - 1971 - New York: Springer Verlag.
  14.  2
    S 3 I andV 2 I.Gaisi Takeuti - 1990 - Archive for Mathematical Logic 29 (3):149-169.
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  15.  20
    Grzegorcyk's Hierarchy and IepΣ1.Gaisi Takeuti - 1994 - Journal of Symbolic Logic 59 (4):1274-1284.
  16.  43
    Transcendence of Cardinals.Gaisi Takeuti - 1965 - Journal of Symbolic Logic 30 (1):1-7.
  17.  29
    Gödel Sentences of Bounded Arithmetic.Gaisi Takeuti - 2000 - Journal of Symbolic Logic 65 (3):1338-1346.
  18.  22
    A Transfer Principle in Harmonic Analysis.Gaisi Takeuti - 1979 - Journal of Symbolic Logic 44 (3):417-440.
  19.  9
    Separations of Theories in Weak Bounded Arithmetic.Gaisi Takeuti - 1995 - Annals of Pure and Applied Logic 71 (1):47-67.
  20.  5
    A Formal System of First-Order Predicate Calculus with Infinitely Long Expressions.Gaisi Takeuti - 1962 - Journal of Symbolic Logic 27 (4):468-468.
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  21. The Critical Number of a Variable in a Function.Gaisi Takeuti - 1994 - Journal of Symbolic Logic 59 (4):1228-1244.
  22.  4
    Construction of the Set Theory From the Theory of Ordinal Numbers.Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):66-67.
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  23.  4
    Grzegorcyk's Hierarchy and $IepSigma_1$.Gaisi Takeuti - 1994 - Journal of Symbolic Logic 59 (4):1274-1284.
  24.  40
    The Universe of Set Theory.Gaisi Takeuti - 1969 - In Kurt Gödel, Jack J. Bulloff, Thomas C. Holyoke & Samuel Wilfred Hahn (eds.), Foundations of Mathematics. New York: Springer. pp. 74--128.
  25.  21
    Formally Self-Referential Propositions for Cut Free Analysis and Related Systems.Georg Kreisel & Gaisi Takeuti - 1985 - Journal of Symbolic Logic 50 (1):244-246.
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  26.  1
    Meetings of the Association for Symbolic Logic, U.S.-Japan Logic Seminar, Tokyo 1969.Gaisi Takeuti - 1971 - Journal of Symbolic Logic 36 (2):357-359.
  27.  6
    A Second Order Version of S2i and U21.Gaisi Takeuti - 1991 - Journal of Symbolic Logic 56 (3):1038-1063.
  28.  19
    Global Intuitionistic Analysis.Gaisi Takeuti & Satoko Titani - 1986 - Annals of Pure and Applied Logic 31:307-339.
  29.  13
    Ordinal Diagrams II.Gaisi Takeuti - 1964 - Journal of Symbolic Logic 29 (3):146-147.
  30.  8
    The Ordinals of the Systems of Second Order Arithmetic with the Provably ▵ 1 2 -Comprehension Axiom and with the ▵ 1 2 - Comprehension Axiom Respectively. [REVIEW]Gaisi Takeuti & Mariko Yasugi - 1983 - Journal of Symbolic Logic 48 (3):877-878.
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  31.  5
    A Metamathematical Theorem on the Theory of Ordinal Numbers.Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):62-62.
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  32.  2
    Ordinal Diagrams.Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):64-65.
  33.  9
    Incompleteness Theorems and S I 2 Versus S I+1 2Godel Sentences of Bounded Arithmetic.Arnold Beckmann & Gaisi Takeuti - 2002 - Bulletin of Symbolic Logic 8 (3):433.
  34. Weaves.Barry Burd & Gaisi Takeuti - 1977 - Annals of the Japan Association for Philosophy of Science 5 (2):47-56.
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  35.  17
    Meeting of the Association for Symbolic Logic, Chicago, 1977.Carl G. Jockusch, Robert I. Soare, William Tait & Gaisi Takeuti - 1978 - Journal of Symbolic Logic 43 (3):614 - 619.
  36.  26
    Two Interpolation Theorems for a Π11 Predicate Calculus.Shoji Maehara & Gaisi Takeuti - 1971 - Journal of Symbolic Logic 36 (2):262 - 270.
  37. Logic Symposia, Hakone, 1979, 1980: Proceedings of Conferences Held in Hakone, Japan, March 21-24, 1979 and February 4-7, 1980. [REVIEW]G. H. Müller, Gaisi Takeuti & T. Tugué (eds.) - 1981 - Springer Verlag.
  38. A Metamathematical Theorem on Functions.Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):65-66.
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  39.  6
    Axioms of Infinity of Set Theory.Gaisi Takeuti - 1962 - Journal of Symbolic Logic 27 (3):354-355.
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  40.  5
    A Remark on Gentzen's Paper "Beweisbarkeit Und Unbeweisbarkeit von Anfangsfallen der Transfiniten Induktion in der Reinen Zahlentheorie." I-II.Gaisi Takeuti - 1964 - Journal of Symbolic Logic 29 (1):58-59.
  41.  5
    A Relativization of Axioms of Strong Infinity to ^|^Omega;1.Gaisi Takeuti - 1970 - Annals of the Japan Association for Philosophy of Science 3 (5):191-204.
  42. A Second Order Version of S I 2 and U 1 2.Gaisi Takeuti - 1991 - Journal of Symbolic Logic 56 (3):1038.
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  43. Construction of Ramified Real Numbers.Gaisi Takeuti - 1957 - Journal of Symbolic Logic 22 (4):352-352.
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  44.  2
    Construction of Ramified Real Numbers.Gaisi Takeuti - 1956 - Annals of the Japan Association for Philosophy of Science 1 (1):41-61.
  45. Forcing on Bounded Arithmetic II.Gaisi Takeuti & Masahiro Yasumoto - 1998 - Journal of Symbolic Logic 63 (3):860-868.
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  46.  20
    Foundations of Mathematics.Gaisi Takeuti & Setsuya Seki - 1959 - Journal of Symbolic Logic 24 (1):73.
  47. Frege Proof System and TNC°.Gaisi Takeuti - 1998 - Journal of Symbolic Logic 63 (2):709 - 738.
    A Frege proof systemFis any standard system of prepositional calculus, e.g., a Hilbert style system based on finitely many axiom schemes and inference rules. An Extended Frege systemEFis obtained fromFas follows. AnEF-sequence is a sequence of formulas ψ1, …, ψκsuch that eachψiis either an axiom ofF, inferred from previous ψuand ψv by modus ponens or of the formq↔ φ, whereqis an atom occurring neither in φ nor in any of ψ1,…,ψi−1. Suchq↔ φ, is called an extension axiom andqa new extension (...)
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  48.  8
    Frege Proof System and TNC$^Circ$.Gaisi Takeuti - 1998 - Journal of Symbolic Logic 63 (2):709-738.
    A Frege proof systemFis any standard system of prepositional calculus, e.g., a Hilbert style system based on finitely many axiom schemes and inference rules. An Extended Frege systemEFis obtained fromFas follows. AnEF-sequence is a sequence of formulas ψ1, …, ψκsuch that eachψiis either an axiom ofF, inferred from previous ψuand ψv by modus ponens or of the formq↔ φ, whereqis an atom occurring neither in φ nor in any of ψ1,…,ψi−1. Suchq↔ φ, is called an extension axiom andqa new extension (...)
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  49. Godel Sentences of Bounded Arithmetic.Gaisi Takeuti - 2000 - Journal of Symbolic Logic 65 (3):1338-1346.
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  50.  7
    Incompleteness Theorems and S I 2 Versus S I+1 2.Gaisi Takeuti - 2002 - Bulletin of Symbolic Logic 8 (3):433-435.