67 found
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  1. Proof Theory.Gaisi Takeuti - 1987 - Elsevier.
  2. Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
     
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  3. Two Applications of Logic to Mathematics.Gaisi Takeuti - 1978 - Princeton University Press.
  4.  15
    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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  5.  80
    Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set Theory.Gaisi Takeuti & Satoko Titani - 1984 - Journal of Symbolic Logic 49 (3):851-866.
  6. Boolean Simple Groups and Boolean Simple Rings.Gaisi Takeuti - 1988 - Journal of Symbolic Logic 53 (1):160-173.
  7.  10
    Globalization of Intui Tionistic Set Theory.Gaisi Takeuti & Satoko Titani - 1987 - Annals of Pure and Applied Logic 33 (2):195-211.
  8.  9
    Fuzzy Logic and Fuzzy Set Theory.Gaisi Takeuti & Satoko Titani - 1992 - Archive for Mathematical Logic 32 (1):1-32.
  9. Meetings of the Association for Symbolic Logic.Gaisi Takeuti - 1971 - Journal of Symbolic Logic 36 (2):357-384.
  10.  6
    Bounded Arithmetic and Truth Definition.Gaisi Takeuti - 1988 - Annals of Pure and Applied Logic 39 (1):75-104.
  11.  86
    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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  12. Frege Proof System and TNC°.Gaisi Takeuti - 1998 - Journal of Symbolic Logic 63 (2):709 - 738.
  13. The Critical Number of a Variable in a Function.Gaisi Takeuti - 1994 - Journal of Symbolic Logic 59 (4):1228-1244.
  14.  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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  15.  20
    Forcing on Bounded Arithmetic II.Gaisi Takeuti & Masahiro Yasumoto - 1998 - Journal of Symbolic Logic 63 (3):860-868.
  16.  19
    Grzegorcyk's Hierarchy and IepΣ1.Gaisi Takeuti - 1994 - Journal of Symbolic Logic 59 (4):1274-1284.
  17.  28
    Gödel Sentences of Bounded Arithmetic.Gaisi Takeuti - 2000 - Journal of Symbolic Logic 65 (3):1338-1346.
  18.  29
    A Formalization of the Theory of Ordinal Numbers.Gaisi Takeuti - 1965 - Journal of Symbolic Logic 30 (3):295-317.
  19.  7
    On a Generalized Logic Calculus.Gaisi Takeuti - 1957 - Journal of Symbolic Logic 22 (4):351-352.
  20.  1
    S 3 I andV 2 I.Gaisi Takeuti - 1990 - Archive for Mathematical Logic 29 (3):149-169.
    No categories
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  21.  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.
  22. Jan Krajíèek.Gaisi Takeuti - 1991 - Annals of Pure and Applied Logic 52:143-153.
     
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  23.  6
    Separations of Theories in Weak Bounded Arithmetic.Gaisi Takeuti - 1995 - Annals of Pure and Applied Logic 71 (1):47-67.
  24.  5
    A Second Order Version of S2i and U21.Gaisi Takeuti - 1991 - Journal of Symbolic Logic 56 (3):1038-1063.
  25.  4
    Grzegorcyk's Hierarchy and $IepSigma_1$.Gaisi Takeuti - 1994 - Journal of Symbolic Logic 59 (4):1274-1284.
  26.  36
    Transcendence of Cardinals.Gaisi Takeuti - 1965 - Journal of Symbolic Logic 30 (1):1-7.
  27.  20
    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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  28.  19
    Foundations of Mathematics.Gaisi Takeuti & Setsuya Seki - 1959 - Journal of Symbolic Logic 24 (1):73.
  29.  19
    Seki Setsuya. Syûgôron Nyûmon . Baifukan, Kanda-Nisikityô, Tokyo 1957, 172 Pp. [REVIEW]Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):73-73.
  30.  11
    Global Intuitionistic Analysis.Gaisi Takeuti & Satoko Titani - 1986 - Annals of Pure and Applied Logic 31 (2):307-339.
  31.  7
    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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  32.  17
    A Transfer Principle in Harmonic Analysis.Gaisi Takeuti - 1979 - Journal of Symbolic Logic 44 (3):417-440.
  33.  3
    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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  34.  9
    Ordinal Diagrams II.Gaisi Takeuti - 1964 - Journal of Symbolic Logic 29 (3):146-147.
  35.  13
    Seki Setsuya. Kisoron . Oyama-Syoten, Tiyoda-Huzimityô, Tokyo 1955, 71 Pp. [REVIEW]Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):73-73.
  36. 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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  37.  9
    Introduction to Axiomatic Set Theory.Gaisi Takeuti - 1971 - New York: Springer Verlag.
  38. On the Theory of Ordinal Numbers.Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):67-67.
  39.  11
    Seki Setsuya. Symposium Hôkokusyû . Kisoron Bunkakai Nihon Sûgakukai, Tokyo 1959, 47 Pp. [REVIEW]Gaisi Takeuti - 1960 - Journal of Symbolic Logic 25 (2):160-161.
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  40.  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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  41.  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.
  42.  3
    A Metamathematical Theorem on the Theory of Ordinal Numbers.Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):62-62.
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  43.  24
    Two Interpolation Theorems for a Π11 Predicate Calculus.Shoji Maehara & Gaisi Takeuti - 1971 - Journal of Symbolic Logic 36 (2):262 - 270.
  44.  2
    Ordinal Diagrams.Gaisi Takeuti - 1959 - Journal of Symbolic Logic 24 (1):64-65.
  45.  7
    Frege Proof System and TNC$^Circ$.Gaisi Takeuti - 1998 - Journal of Symbolic Logic 63 (2):709-738.
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  46.  15
    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.
  47.  6
    Axioms of Infinity of Set Theory.Gaisi Takeuti - 1962 - Journal of Symbolic Logic 27 (3):354-355.
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  48.  6
    Incompleteness Theorems and S I 2 Versus S I+1 2.Gaisi Takeuti - 2002 - Bulletin of Symbolic Logic 8 (3):433-435.
  49.  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.
  50.  4
    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.
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