33 found
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  1. Georg Kreisel (1967). Informal Rigour and Completeness Proofs. In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland 138--157.
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  2.  22
    Georg Kreisel & Azriel Lévy (1968). Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems. Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14 (1):97--142.
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  3. Georg Kreisel (1959). Interpretation of Analysis by Means of Constructive Functionals of Finite Types. In A. Heyting (ed.), Constructivity in Mathematics. Amsterdam, North-Holland Pub. Co. 101--128.
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  4.  6
    Georg Kreisel (1967). Elements of Mathematical Logic. Amsterdam, North Holland Pub. Co..
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  5.  78
    Georg Kreisel (1987). Church's Thesis and the Ideal of Informal Rigour. Notre Dame Journal of Formal Logic 28 (4):499-519.
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  6.  7
    Georg Kreisel (1967). Mathematical Logic. Journal of Symbolic Logic 32 (3):419-420.
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  7.  15
    Georg Kreisel & William W. Tait (1961). Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (1-5):28-38.
  8.  75
    Georg Kreisel (1985). Mathematical Logic: Tool and Object Lesson for Science. Synthese 62 (2):139-151.
    The object lesson concerns the passage from the foundational aims for which various branches of modern logic were originally developed to the discovery of areas and problems for which logical methods are effective tools. The main point stressed here is that this passage did not consist of successive refinements, a gradual evolution by adaptation as it were, but required radical changes of direction, to be compared to evolution by migration. These conflicts are illustrated by reference to set theory, model theory, (...)
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  9.  47
    Georg Kreisel (1991). Review: Kurt Godel, Solomon Feferman, John W. Dawson, Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, Jean van Heijenoort, Collected Works of Kurt Godel 1938-1974. [REVIEW] Journal of Symbolic Logic 56 (3):1085-1089.
  10.  6
    Georg Kreisel (1958). Hilbert's programme. Dialectica 12 (3‐4):346-372.
    Hilbert's plan for understanding the concept of infinity required the elimination of non‐finitist machinery from proofs of finitist assertions. The failure of the original plan leads to a hierarchy of progressively less elementary, but still constructive methods instead of finitist ones . A mathematical proof of this failure requires a definition of « finitist ».—The paper sketches the three principal methods for the syntactic analysis of non‐constructive mathematics, the resulting consistency proofs and constructive interpretations, modelled on Herbrand's theorem, and their (...)
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  11.  29
    Georg Kreisel (1978). The Motto of 'Philosophical Investigations' and the Philosophy of Proofs and Rules. Grazer Philosophische Studien 6:13-38.
    Ausgangspunkt dieses Artikels ist die Einsicht, die auch von Wittgenstein und der "schweigenden Mehrheit" geteilt wird, daß die meisten sogenannten fundamentalen Begriffe und Probleme der Philosophie erkenntnistheoretisch unrentabel sind, insbesondere der Begriff der Gültigkeit (von Beweis- und Rechenregeln) und seine traditionelle Problematik. Im Gegensatz zu Wittgenstein wird diese Einsicht aber nicht auf "Sinnlosigkeit", d.h. Präzisionsunfähigkeitjener Problematik, sondern auf ihre Oberflächl d.h. unangemessene Allgemeinheit, zurückgeführt.
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  12.  1
    Georg Kreisel & Daniel Lacombe (1966). Ensembles Récursivement Mesurable Et Ensembles Récursivement Ouverts Ou Fermés. Journal of Symbolic Logic 31 (1):133-133.
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  13.  8
    Georg Kreisel (1972). Review: Hilary Putnam, Mathematics Without Foundations. [REVIEW] Journal of Symbolic Logic 37 (2):402-404.
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  14.  8
    Georg Kreisel (2011). Logical Hygiene, Foundations, and Abstractions: Diversity Among Aspects and Options. In Matthias Baaz (ed.), Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press 27.
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  15.  23
    Georg Kreisel (1987). Book Review: Collected Works, Vol. I [Oxford Univ. Press, New York, 1986] by K. Gödel. [REVIEW] Notre Dame Journal of Formal Logic 29 (1):160-181.
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  16.  4
    Georg Kreisel (1960). Review: Kurt Schutte, Beweistheorie. [REVIEW] Journal of Symbolic Logic 25 (3):243-249.
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  17. Georg Kreisel & J. L. Krivine (1967). Éléments de Logique Mathématique Théorie des Modèles. Dunod.
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  18.  2
    Georg Kreisel (1970). Review: S. Ju. Maslov, G. E. Minc, V. P. Orevkov, E. Mendelson, Unsolvability in the Constructive Predicate Calculus of Certain Classes of Formulas Containing Only Monadic Predicate Variables. [REVIEW] Journal of Symbolic Logic 35 (1):143-144.
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  19.  3
    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.  2
    Georg Kreisel (1975). Review: Solomon Feferman, Ordinals and Functionals in Proof Theory. [REVIEW] Journal of Symbolic Logic 40 (4):625-626.
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  21.  3
    Georg Kreisel (1974). Review: Hao Wang, Logic, Computation and Philosophy. [REVIEW] Journal of Symbolic Logic 39 (2):358-359.
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  22.  1
    Georg Kreisel, G. Kreisel & A. Heyting (1971). Gödel's Intepretation of Heyting's Arithmetic. Journal of Symbolic Logic 36 (1):169-171.
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  23.  1
    Georg Kreisel (1966). Some Concepts Concerning Formal Systems of Number Theory. Journal of Symbolic Logic 31 (1):128-128.
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  24. Georg Kreisel (1966). Review: N. A. Sanin, On the Constructive Interpretation of Mathematical Judgments; S. C. Kleene, A Formal System of Intuitionistic Analysis. [REVIEW] Journal of Symbolic Logic 31 (2):258-261.
     
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  25. Georg Kreisel (1966). Šanin N. A.. On the Constructive Interpretation of Mathematical Judgments. English Translation of XXXI 255 by Mendelson Elliott. American Mathematical Society Translations, Ser. 2 Vol. 23 , Pp. 109–189.Markov A. A.. On Constructive Functions. English Translation of XXXI 258 by Machover Moshe. American Mathematical Society Translations, Vol. 29 , Pp. 163–195.Kleene S. C.. A Formal System of Intuitionistic Analysis. The Foundations of Intuitionistlc Mathematics Especially in Relation to Recursive Functions, by Kleene Stephen Cole and Vesley Richard Eugene, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam 1965, Pp. 1–89.Kleene S. C.. Various Notions of Realizability: The Foundations of Intuitionistlc Mathematics Especially in Relation to Recursive Functions, by Kleene Stephen Cole and Vesley Richard Eugene, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam 1965, Pp. 90–132.Vesley Richard E.. The. [REVIEW] Journal of Symbolic Logic 31 (2):258-261.
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  26. Georg Kreisel (1988). Book Review: "Kurt Gödel, Collected Works, Vol. I". [REVIEW] Notre Dame Journal of Formal Logic 29:160-181.
     
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  27. Georg Kreisel, Kurt Godel, Solomon Feferman, John W. Dawson, Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay & Jean van Heijenoort (1991). Collected Works of Kurt Godel 1938-1974. Journal of Symbolic Logic 56 (3):1085.
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  28. Georg Kreisel (1975). Feferman Solomon. Ordinals and Functionals in Proof Theory. Actes du Congrès International des Mathématiciens 1970, Gauthier-Villars, Paris 1971, Vol. 1, Pp. 229–233. [REVIEW] Journal of Symbolic Logic 40 (4):625-626.
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  29. Georg Kreisel (1970). Maslov S. Ú., Minc G. É., and Orévkov V. P.. Nérazréšimost′ Ν Konstruktivnom Isčislénii Prédikatov Nékotoryh Klassov Formul, Sodéržaščih Tol′Ko Odnoméstnyé Prédikatnyé Péréménnyé. Doklady Akadémii Nauk, Vol. 163 , Pp. 295–297.Maslov S. Ju., Minc G. E., and Orevkov V. P.. Unsolvability in the Constructive Predicate Calculus of Certain Classes of Formulas Containing Only Monadic Predicate Variables. Translation of the Preceding by Mendelson E.. Soviet Mathematics, Vol. 6 , Pp. 918–920. [REVIEW] Journal of Symbolic Logic 35 (1):143-144.
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  30. Georg Kreisel (1972). Putnam Hilary. Mathematics Without Foundations. The Journal of Philosophy, Vol. 64 , Pp. 5–22. Journal of Symbolic Logic 37 (2):402-404.
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  31. Georg Kreisel (1960). Reviews. Kurt Schütte. Beweistheorie. Springer-Verlag, Berlin-Göttingen-Heidelberg 1960, X + 355 pp. [REVIEW] Journal of Symbolic Logic 25 (3):243-249.
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  32. Georg Kreisel (1974). Wang Hao. Logic, Computation and Philosophy. L''ge de la Science, Vol. 3 , Pp. 101–115. Journal of Symbolic Logic 39 (2):358-359.
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  33. 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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