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G. Kreisel [103]Georg Kreisel [34]
  1. Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.
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  2.  38
    Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.G. Kreisel & A. Lévy - 1968 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 14 (7-12):97-142.
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  3.  42
    Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.Georg Kreisel & Azriel Lévy - 1968 - Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14 (1):97--142.
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  4. Interpretation of Analysis by Means of Constructive Functionals of Finite Types.Georg Kreisel - 1959 - In A. Heyting (ed.), Constructivity in Mathematics. Amsterdam: North-Holland Pub. Co.. pp. 101--128.
     
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  5.  19
    Formal Systems for Some Branches of Intuitionistic Analysis.G. Kreisel - 1970 - Annals of Pure and Applied Logic 1 (3):229.
  6.  82
    A Survey of Proof Theory.G. Kreisel - 1968 - Journal of Symbolic Logic 33 (3):321-388.
  7.  71
    The Collected Papers of Gerhard Gentzen.G. Kreisel - 1971 - Journal of Philosophy 68 (8):238-265.
  8.  32
    Mathematical Logic.Georg Kreisel - 1967 - Journal of Symbolic Logic 32 (3):419-420.
  9.  97
    A Notion of Mechanistic Theory.G. Kreisel - 1974 - Synthese 29 (1-4):11 - 26.
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  10. Wittgenstein's Remarks on the Foundations of Mathematics. [REVIEW]G. Kreisel - 1958 - British Journal for the Philosophy of Science 9 (34):135-158.
  11.  2
    Eine Unableitbarkeitsbeweismethode für den intuitionistischen Aussagenkalkul.G. Kreisel - 1957 - Archive for Mathematical Logic 3 (3/4):74.
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  12.  35
    Eduard Wette. Definition Eines Formalen Systems Konstruktiver Arithmetik. Foundations of Mathemattes, Symposium Papers Commemorating the Sixtieth Birthday of Kurt Gödel, Edited by Jack J. Bulloff, Thomas C. Holyoke, and S. W. Hahn, Springer-Verlag New York Inc., 1969, Pp. 130–195. [REVIEW]G. Kreisel & J. Zucker - 1972 - Journal of Symbolic Logic 37 (1):203-204.
  13.  35
    Hilary Putnam. Mathematics Without Foundations. The Journal of Philosophy, Vol. 64 , Pp. 5–22.Georg Kreisel - 1972 - Journal of Symbolic Logic 37 (2):402-404.
  14.  38
    On the Interpretation of Non-Finitist Proofs–Part II.G. Kreisel - 1952 - Journal of Symbolic Logic 17 (1):43-58.
  15.  25
    Metarecursive Sets.G. Kreisel & Gerald E. Sacks - 1965 - Journal of Symbolic Logic 30 (3):318-338.
  16.  42
    On the Interpretation of Non-Finitist Proofs—Part I.G. Kreisel - 1951 - Journal of Symbolic Logic 16 (4):241-267.
  17. 1 — Consistency and Faithful Interpretations.S. Feferman, G. Kreisel & S. Orey - forthcoming - Archive for Mathematical Logic.
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  18.  27
    Transfinite Induction and Bar Induction of Types Zero and One, and the Role of Continuity in Intuitionistic Analysis.W. A. Howard & G. Kreisel - 1966 - Journal of Symbolic Logic 31 (3):325-358.
  19.  43
    On Weak Completeness of Intuitionistic Predicate Logic.G. Kreisel - 1962 - Journal of Symbolic Logic 27 (2):139-158.
  20.  16
    Foundations of Intuitionistic Logic.G. Kreisel - 1965 - Journal of Symbolic Logic 30 (2):243-244.
  21.  15
    Hilbert's programme.Georg Kreisel - 1958 - 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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  22.  17
    A Survey of Mathematical Logic.Georg Kreisel - 1966 - Philosophical Review 75 (2):240-244.
  23.  94
    Church's Thesis and the Ideal of Informal Rigour.Georg Kreisel - 1987 - Notre Dame Journal of Formal Logic 28 (4):499-519.
  24.  56
    Mathematical Significance of Consistency Proofs.G. Kreisel - 1958 - Journal of Symbolic Logic 23 (2):155-182.
  25.  80
    Collected Works of Kurt Godel 1938-1974.Georg Kreisel, Kurt Godel, Solomon Feferman, John W. Dawson, Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay & Jean van Heijenoort - 1991 - Journal of Symbolic Logic 56 (3):1085.
  26.  20
    Saul A. Kripke. Semantical Analysis of Intuitionistic Logic I. Formal Systems and Recursive Functions, Proceedings of the Eighth Logic Colloquium, Oxford, July 1963, Edited by J. N. Crossley and M. A. E. Dummett, Series in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam1965, Pp. 92–130. [REVIEW]G. Kreisel - 1970 - Journal of Symbolic Logic 35 (2):330-332.
  27.  8
    Some Reasons for Generalizing Recursion Theory.G. Kreisel, R. O. Gandy & C. E. M. Yates - 1975 - Journal of Symbolic Logic 40 (2):230-232.
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  28.  78
    Second Thoughts Around Some of Göde's Writings:.G. Kreisel - 1998 - Synthese 114 (1):99-160.
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  29.  22
    Which Number Theoretic Problems Can Be Solved in Recursive Progressions on Π1 1-Paths Through O?G. Kreisel - 1972 - Journal of Symbolic Logic 37 (2):311-334.
  30.  14
    Elements of Mathematical Logic: Model Theory.Georg Kreisel - 1967 - Amsterdam: North Holland Pub. Co..
  31.  11
    A Computable Ordinary Differential Equation with Possesses No Computable Solution.G. Kreisel - 1982 - Journal of Symbolic Logic 47 (4):900-902.
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  32.  16
    Marian Boykan Pour-El and Ian Richards. A Computable Ordinary Differential Equation Which Possesses No Computable Solution, Annals of Mathematical Logic, Vol. 17 , Pp. 61–90. - Marian Boykan Pour-El and Ian Richards. The Wave Equation with Computable Initial Data Such That its Unique Solution is Not Computable. Advances in Mathematics, Vol. 39 , Pp. 215–239. [REVIEW]G. Kreisel - 1982 - Journal of Symbolic Logic 47 (4):900-902.
  33.  20
    Hao Wang. Logic, Computation and Philosophy. L''ge de la Science, Vol. 3 , Pp. 101–115.Georg Kreisel - 1974 - Journal of Symbolic Logic 39 (2):358-359.
  34.  18
    S. Ú. Maslov, G. É. Minc, and V. P. Orévkov. Nérazréšimost′ Ν Konstruktivnom Isčislénii Prédikatov Nékotoryh Klassov Formul, Sodéržaščih Tol′Ko Odnoméstnyé Prédikatnyé Péréménnyé. Doklady Akadémii Nauk, Vol. 163 , Pp. 295–297. - S. Ju. Maslov, G. E. Minc, and V. P. Orevkov. Unsolvability in the Constructive Predicate Calculus of Certain Classes of Formulas Containing Only Monadic Predicate Variables. Translation of the Preceding by E. Mendelson. Soviet Mathematics, Vol. 6 , Pp. 918–920. [REVIEW]Georg Kreisel - 1970 - Journal of Symbolic Logic 35 (1):143-144.
  35.  30
    Number Theoretic Concepts and Recursive Well-Orderings.G. Kreisel, J. Shoenfield & Hao Wang - 1966 - Journal of Symbolic Logic 31 (3):511-512.
  36.  18
    Two Notes on the Foundations of Set‐Theory.G. Kreisel - 1969 - Dialectica 23 (2):93-114.
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  37.  35
    Problems.Heinrich Scholz, G. Kreisel & Leon Henkin - 1952 - Journal of Symbolic Logic 17 (2):160.
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  38.  64
    A Variant to Hilbert's Theory of the Foundations of Arithmetic.G. Kreisel - 1953 - British Journal for the Philosophy of Science 4 (14):107-129.
    IN Hilbert's theory of the foundations of any given branch of mathematics the main problem is to establish the consistency (of a suitable formalisation) of this branch. Since the (intuitionist) criticisms of classical logic, which Hilbert's theory was intended to meet, never even alluded to inconsistencies (in classical arithmetic), and since the investigations of Hilbert's school have always established much more than mere consistency, it is natural to formulate another general problem in the foundations of mathematics: to translate statements of (...)
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  39.  43
    Frege’s Foundations and Intuitional Logic.G. Kreisel - 1984 - The Monist 67 (1):72-91.
    Summary. This article develops two principal points. First, the so-called rivals of logical foundations, associated with Zermelo, Hilbert, and Brouwer, are here regarded as variants; specifically: to simplify, refine, resp. extend Frege’s scheme. Each of the variations is seen as a special case of a familiar strategy in the pursuit of knowledge. In particular, the extension provided by Brouwer’s intuitionistic logic concerns the class of propositions considered: about incompletely defined objects such as choice sequences. In contrast, Frege or, for that (...)
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  40. Principles of Proof, Etc.G. Kreisel - 1970 - In A. Kino, John Myhill & Richard Eugene Vesley (eds.), Intuitionism and Proof Theory. Amsterdam: North-Holland Pub. Co.. pp. 489--5.
     
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  41. Mathematical Interpretation of Formal Systems.Th Skolem, G. Hasenjaeger, G. Kreisel, A. Robinson, H. Wang, L. Henkin & J. Łoś (eds.) - 1955 - North-Holland Pub. Co..
  42.  30
    A Remark on Free Choice Sequences and the Topological Completeness Proofs.G. Kreisel - 1958 - Journal of Symbolic Logic 23 (4):369-388.
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  43.  14
    N. A. Šanin. On the Constructive Interpretation of Mathematical Judgments. English Translation of XXXI 255 by Elliott Mendelson. American Mathematical Society Translations, Ser. 2 Vol. 23 , Pp. 109–189. - A. A. Markov. On Constructive Functions. English Translation of XXXI 258 by Moshe Machover. American Mathematical Society Translations, Vol. 29 , Pp. 163–195. - S. C. Kleene. A Formal System of Intuitionistic Analysis. The Foundations of Intuitionistlc Mathematics Especially in Relation to Recursive Functions, by Stephen Cole Kleene and Richard Eugene Vesley, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam1965, Pp. 1–89. - S. C. Kleene. Various Notions of Realizability:The Foundations of Intuitionistlc Mathematics Especially in Relation to Recursive Functions, by Stephen Cole Kleene and Richard Eugene Vesley, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam1965, Pp. 90–132. - Richard E. Ve. [REVIEW]Georg Kreisel - 1966 - Journal of Symbolic Logic 31 (2):258-261.
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  44.  10
    Recent Results in Set Theory.Andrzej Mostowski, Imre Lakatos, G. Kreisel, A. Robinson & A. Mostowski - 1972 - Journal of Symbolic Logic 37 (4):765-766.
  45.  87
    Mathematical Logic: Tool and Object Lesson for Science.Georg Kreisel - 1985 - 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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  46.  20
    Set Existence.R. O. Gandy, G. Kreisel & W. W. Tait - 1962 - Journal of Symbolic Logic 27 (2):232-233.
  47.  10
    Solomon Feferman. Ordinals and Functionals in Proof Theory. Actes du Congrès International des Mathématiciens 1970, Gauthier-Villars, Paris 1971, Vol. 1, Pp. 229–233. [REVIEW]Georg Kreisel - 1975 - Journal of Symbolic Logic 40 (4):625-626.
  48.  4
    Persistent and Invariant Formulas Relative to Theories of Higher Order.S. Feferman, G. Kreisel & Solomon Feferman - 1972 - Journal of Symbolic Logic 37 (4):764-765.
  49.  26
    Finite Definability of Number-Theoretic Functions and Parametric Completeness of Equational Calculi.Georg Kreisel & William W. Tait - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (1-5):28-38.
  50.  13
    Mathematical Problems. Lecture Delivered Before the International Congress of Mathematicians at Paris in 1900.David Hilbert, Mary Winston Newsom, Felix E. Browder, Donald A. Martin, G. Kreisel & Martin Davis - 1979 - Journal of Symbolic Logic 44 (1):116-119.
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