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G. Kreisel [104]Georg Kreisel [35]
  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.  52
    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. 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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  4.  47
    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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  5.  45
    Mathematical Logic.Georg Kreisel - 1967 - Journal of Symbolic Logic 32 (3):419-420.
  6. A Survey of Proof Theory.G. Kreisel - 1968 - Journal of Symbolic Logic 33 (3):321-388.
  7.  20
    Formal Systems for Some Branches of Intuitionistic Analysis.G. Kreisel - 1970 - Annals of Mathematical Logic 1 (3):229.
  8.  83
    The Collected Papers of Gerhard Gentzen.G. Kreisel - 1971 - Journal of Philosophy 68 (8):238-265.
  9. Wittgenstein's Remarks on the Foundations of Mathematics. [REVIEW]G. Kreisel - 1958 - British Journal for the Philosophy of Science 9 (34):135-158.
  10.  20
    Foundations of Intuitionistic Logic.G. Kreisel - 1965 - Journal of Symbolic Logic 30 (2):243-244.
  11.  50
    On Weak Completeness of Intuitionistic Predicate Logic.G. Kreisel - 1962 - Journal of Symbolic Logic 27 (2):139-158.
  12.  43
    On the Interpretation of Non-Finitist Proofs–Part II.G. Kreisel - 1952 - Journal of Symbolic Logic 17 (1):43-58.
  13.  46
    On the Interpretation of Non-Finitist Proofs—Part I.G. Kreisel - 1951 - Journal of Symbolic Logic 16 (4):241-267.
  14.  99
    A Notion of Mechanistic Theory.G. Kreisel - 1974 - Synthese 29 (1-4):11 - 26.
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  15.  28
    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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  16.  18
    Elements of Mathematical Logic: Model Theory.Georg Kreisel - 1967 - Amsterdam: North Holland Pub. Co..
  17.  2
    Eine Unableitbarkeitsbeweismethode für den intuitionistischen Aussagenkalkul.G. Kreisel - 1957 - Archive for Mathematical Logic 3 (3-4):74.
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  18.  67
    Mathematical Significance of Consistency Proofs.G. Kreisel - 1958 - Journal of Symbolic Logic 23 (2):155-182.
  19.  29
    Metarecursive Sets.G. Kreisel & Gerald E. Sacks - 1965 - Journal of Symbolic Logic 30 (3):318-338.
    Our ultimate purpose is to give an axiomatic treatment of recursion theory sufficient to develop the priority method. The direct or abstract approach is to keep in mind as clearly as possible the methods actually used in recursion theory, and then to formulate them explicitly. The indirect or experimental approach is to look first for other mathematical theories which seem similar to recursion theory, to formulate the analogies precisely, and then to search for an axiomatic treatment which covers not only (...)
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  20.  29
    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.
  21. Church's Thesis and the Ideal of Informal Rigour.Georg Kreisel - 1987 - Notre Dame Journal of Formal Logic 28 (4):499-519.
  22.  19
    A Survey of Mathematical Logic.Georg Kreisel - 1966 - Philosophical Review 75 (2):240-244.
  23.  2
    Number Theoretic Concepts and Recursive Well-Orderings.G. Kreisel, J. Shoenfield & Hao Wang - 1960 - Archive for Mathematical Logic 5 (1-2):42-64.
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  24.  83
    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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  25.  39
    Problems.Heinrich Scholz, G. Kreisel & Leon Henkin - 1952 - Journal of Symbolic Logic 17 (2):160.
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  26.  1
    Mathematical Interpretation of Formal Systems.Thoralf Skolem, G. Hasenjaeger, G. Kreisel, A. Robinson, Hao Wang, L. Henkin & J. Łoś (eds.) - 1955 - Amsterdam, Netherlands: North-Holland Pub. Co..
  27.  11
    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.  35
    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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  29.  7
    Hilbert's Programme.Georg Kreisel - 1962 - Journal of Symbolic Logic 27 (2):228-229.
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  30.  24
    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.
  31.  19
    Two Notes on the Foundations of Set‐Theory.G. Kreisel - 1969 - Dialectica 23 (2):93-114.
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  32.  64
    1 — Consistency and Faithful Interpretations.S. Feferman, G. Kreisel & S. Orey - 1962 - Archive for Mathematical Logic 6 (1-2):52-63.
  33. 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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  34.  31
    Number Theoretic Concepts and Recursive Well-Orderings.G. Kreisel, J. Shoenfield & Hao Wang - 1966 - Journal of Symbolic Logic 31 (3):511-512.
  35.  12
    Recent Results in Set Theory.Andrzej Mostowski, Imre Lakatos, G. Kreisel, A. Robinson & A. Mostowski - 1972 - Journal of Symbolic Logic 37 (4):765-766.
  36.  13
    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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  37.  28
    Set Existence.R. O. Gandy, G. Kreisel & W. W. Tait - 1962 - Journal of Symbolic Logic 27 (2):232-233.
  38.  38
    Elementary Completeness Properties of Intuitionistic Logic with a Note on Negations of Prenex Formulae.G. Kreisel - 1958 - Journal of Symbolic Logic 23 (3):317-330.
  39.  6
    Mathematical Significance of Consistency Proofs.G. Kreisel - 1966 - Journal of Symbolic Logic 31 (1):129-129.
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  40.  93
    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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  41.  19
    On a Problem of Henkin's.G. Kreisel - 1954 - Journal of Symbolic Logic 19 (3):219-220.
  42.  79
    Second Thoughts Around Some of Göde's Writings:.G. Kreisel - 1998 - Synthese 114 (1):99-160.
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  43. Reply to Professor Bar-Hillel.G. Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. Amsterdam: North-Holland Pub. Co.. pp. 175--178.
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  44.  32
    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.
  45.  7
    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.
  46.  17
    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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  47.  14
    Some Applications of Formalized Consistency Proofs.G. Kreisel & Hao Wang - 1956 - Journal of Symbolic Logic 21 (4):404-405.
  48.  2
    On Weak Completeness of Intuitionistic Predicate Logic.G. Kreisel - 1969 - Journal of Symbolic Logic 34 (1):119-120.
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  49. What Can Be Done for Mathematical Logic.G. Kreisel - 1967 - In Ralph Schoenman (ed.), Bertrand Russell: Philosopher of the Century. pp. 273--303.
     
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  50.  47
    Some Uses of Mathematics.G. Kreisel - 1956 - British Journal for the Philosophy of Science 7 (26):161-173.
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