68 found
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  1. Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
     
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  2. Gaisi Takeuti (1971). Meetings of the Association for Symbolic Logic. Journal of Symbolic Logic 36 (2):357-384.
  3. Gaisi Takeuti (1988). Boolean Simple Groups and Boolean Simple Rings. Journal of Symbolic Logic 53 (1):160-173.
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  4. Gaisi Takeuti (1978). Two Applications of Logic to Mathematics. Princeton University Press.
     
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  5. Gaisi Takeuti (1998). Frege Proof System and TNC⚬. Journal of Symbolic Logic 63 (2):709 - 738.
  6.  28
    Gaisi Takeuti (1969). The Universe of Set Theory. In Kurt Gödel, Jack J. Bulloff, Thomas C. Holyoke & Samuel Wilfred Hahn (eds.), Foundations of Mathematics. New York, Springer 74--128.
  7.  1
    Jan Krajíček, Pavel Pudlák & Gaisi Takeuti (1991). Bounded Arithmetic and the Polynomial Hierarchy. 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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  8. Gaisi Takeuti (1994). The Critical Number of a Variable in a Function. Journal of Symbolic Logic 59 (4):1228-1244.
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  9.  57
    Gaisi Takeuti & Satoko Titani (1984). Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set Theory. Journal of Symbolic Logic 49 (3):851-866.
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  10.  17
    Gaisi Takeuti (1990). S 3 I andV 2 I (BD). Archive for Mathematical Logic 29 (3):149-169.
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  11.  13
    Gaisi Takeuti (1991). Jan Krajíèek. Annals of Pure and Applied Logic 52:143-153.
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  12.  49
    Gaisi Takeuti (1985). Proof Theory and Set Theory. 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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  13.  6
    Gaisi Takeuti & Satoko Titani (1992). Fuzzy Logic and Fuzzy Set Theory. Archive for Mathematical Logic 32 (1):1-32.
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  14.  4
    Gaisi Takeuti & Satoko Titani (1987). Globalization of Intui Tionistic Set Theory. Annals of Pure and Applied Logic 33 (2):195-211.
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  15.  14
    Gaisi Takeuti (2000). Gödel Sentences of Bounded Arithmetic. Journal of Symbolic Logic 65 (3):1338-1346.
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  16.  2
    Gaisi Takeuti (1988). Bounded Arithmetic and Truth Definition. Annals of Pure and Applied Logic 39 (1):75-104.
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  17.  6
    Gaisi Takeuti & Masahiro Yasumoto (1998). Forcing on Bounded Arithmetic II. Journal of Symbolic Logic 63 (3):860-868.
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  18.  3
    Gaisi Takeuti (1991). A Second Order Version of Si2 and U12. Journal of Symbolic Logic 56 (3):1038-1063.
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  19.  2
    Georg Kreisel & Gaisi Takeuti (1985). Formally Self-Referential Propositions for Cut Free Analysis and Related Systems. Journal of Symbolic Logic 50 (1):244-246.
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  20.  6
    Gaisi Takeuti (1965). A Formalization of the Theory of Ordinal Numbers. Journal of Symbolic Logic 30 (3):295-317.
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  21.  4
    Gaisi Takeuti & Satoko Titani (1986). Global Intuitionistic Analysis. Annals of Pure and Applied Logic 31 (2):307-339.
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  22.  10
    Gaisi Takeuti (1965). Transcendence of Cardinals. Journal of Symbolic Logic 30 (1):1-7.
  23.  6
    Gaisi Takeuti (1979). A Transfer Principle in Harmonic Analysis. Journal of Symbolic Logic 44 (3):417-440.
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  24.  8
    Gaisi Takeuti (1994). Grzegorcyk's Hierarchy and Iepσ. Journal of Symbolic Logic 59 (4):1274 - 1284.
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  25.  10
    Shoji Maehara & Gaisi Takeuti (1971). Two Interpolation Theorems for a Π11 Predicate Calculus. Journal of Symbolic Logic 36 (2):262 - 270.
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  26. Gaisi Takeuti (1995). Separations of Theories in Weak Bounded Arithmetic. Annals of Pure and Applied Logic 71 (1):47-67.
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  27.  1
    Gaisi Takeuti (1959). On the Fundamental Conjecture of GLC. Journal of Symbolic Logic 24 (1):62-64.
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  28. Gaisi Takeuti (1959). Review: Setsuya Seki, Introduction to Set Theory. [REVIEW] Journal of Symbolic Logic 24 (1):73-73.
     
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  29.  5
    Carl G. Jockusch Jr, Robert I. Soare, William Tait & Gaisi Takeuti (1978). Meeting of the Association for Symbolic Logic: Chicago, 1977. Journal of Symbolic Logic 43 (3):614 - 619.
  30. Gaisi Takeuti & Mariko Yasugi (1983). 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] Journal of Symbolic Logic 48 (3):877-878.
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  31. Gaisi Takeuti (1967). Review: Kurt Schutte, Syntactical and Semantical Properties of Simple Type Theory. [REVIEW] Journal of Symbolic Logic 32 (3):418-419.
     
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  32. Gaisi Takeuti (1964). Ordinal Diagrams II. Journal of Symbolic Logic 29 (3):146-147.
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  33. Gaisi Takeuti (1959). A Metamathematical Theorem on the Theory of Ordinal Numbers. Journal of Symbolic Logic 24 (1):62-62.
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  34. Gaisi Takeuti (1959). Ordinal Diagrams. Journal of Symbolic Logic 24 (1):64-65.
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  35. Gaisi Takeuti (1957). On a Generalized Logic Calculus. Journal of Symbolic Logic 22 (4):351-352.
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  36. Arnold Beckmann & Gaisi Takeuti (2002). Incompleteness Theorems and S I 2 Versus S I+1 2Godel Sentences of Bounded Arithmetic. Bulletin of Symbolic Logic 8 (3):433.
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  37. Barry Burd & Gaisi Takeuti (1977). Weaves. Annals of the Japan Association for Philosophy of Science 5 (2):47-56.
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  38. G. H. Müller, Gaisi Takeuti & T. Tugué (eds.) (1981). Logic Symposia, Hakone, 1979, 1980: Proceedings of Conferences Held in Hakone, Japan, March 21-24, 1979 and February 4-7, 1980. [REVIEW] Springer-Verlag.
     
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  39. Dag Prawitz, Gaisi Takeuti, Georg Kreisel, Wolfram Pohlers, Stephen G. Simpson & Solomon Feferman (1991). Proof Theory.Proof Theory: Some Personal Recollections.Contributions of the Schutte School in Munich to Proof Theory.Subsystems of Z 2 and Reverse Mathematics.Proof Theory: A Personal Report. [REVIEW] Journal of Symbolic Logic 56 (3):1094.
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  40. Gaisi Takeuti (1962). A Formal System of First-Order Predicate Calculus with Infinitely Long Expressions. Journal of Symbolic Logic 27 (4):468-468.
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  41. Gaisi Takeuti (1959). A Metamathematical Theorem on Functions. Journal of Symbolic Logic 24 (1):65-66.
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  42. Gaisi Takeuti (1962). Axioms of Infinity of Set Theory. Journal of Symbolic Logic 27 (3):354-355.
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  43. Gaisi Takeuti (1964). A Remark on Gentzen's Paper "Beweisbarkeit Und Unbeweisbarkeit von Anfangsfallen der Transfiniten Induktion in der Reinen Zahlentheorie." I-II. Journal of Symbolic Logic 29 (1):58-59.
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  44. Gaisi Takeuti (1970). A Relativization of Axioms of Strong Infinity to ^|^Omega;1. Annals of the Japan Association for Philosophy of Science 3 (5):191-204.
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  45. Gaisi Takeuti (1991). A Second Order Version of S I 2 and U 1 2. Journal of Symbolic Logic 56 (3):1038.
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  46. Gaisi Takeuti (1988). Boolean Simple Groups and Boolean Simple Rings. Journal of Symbolic Logic 53 (1):160-173.
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  47. Gaisi Takeuti (1957). Construction of Ramified Real Numbers. Journal of Symbolic Logic 22 (4):352-352.
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  48. Gaisi Takeuti (1956). Construction of Ramified Real Numbers. Annals of the Japan Association for Philosophy of Science 1 (1):41-61.
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  49. Gaisi Takeuti (1959). Construction of the Set Theory From the Theory of Ordinal Numbers. Journal of Symbolic Logic 24 (1):66-67.
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  50. Gaisi Takeuti & Setsuya Seki (1959). Foundations of Mathematics. Journal of Symbolic Logic 24 (1):73.
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