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R. L. Goodstein [66]R. Louis Goodstein [2]
  1.  40
    On the restricted ordinal theorem.R. L. Goodstein - 1944 - Journal of Symbolic Logic 9 (2):33-41.
    The proposition that a decreasing sequence of ordinals necessarily terminates has been given a new, and perhaps unexpected, importance by the rôle which it plays in Gentzen's proof of the freedom from contradiction of the “reine Zahlentheorie.” Gödel's construction of non-demonstrable propositions and the establishment of the impossibility of a proof of freedom from contradiction, within the framework of a certain type of formal system, showed that a proof of freedom from contradiction could be found only by transcending the axioms (...)
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  2.  31
    Recursive Number Theory. A Development of Recursive Arithmetic in a Logic-Free Equation Calculus.R. L. Goodstein - 1958 - Journal of Symbolic Logic 23 (2):227-228.
  3.  14
    Function Theory in an Axiom-free Equation Calculus.R. L. Goodstein - 1946 - Journal of Symbolic Logic 11 (1):24-26.
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  4. Constructive formalism.R. L. Goodstein - 1951 - Leicester [Eng.]: University College.
  5.  20
    On the formalisation of indirect discourse.R. L. Goodstein - 1958 - Journal of Symbolic Logic 23 (4):417-419.
  6.  4
    On the Restricted Ordinal Theorem.R. L. Goodstein - 1945 - Journal of Symbolic Logic 10 (3):104-105.
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  7.  76
    The significance of incompleteness theorems.R. L. Goodstein - 1963 - British Journal for the Philosophy of Science 14 (55):208-220.
  8. Essays in the philosophy of mathematics.R. L. Goodstein - 1965 - [Leicester, Eng.]: Leicester University Press.
  9.  11
    Recursive analysis.R. L. Goodstein - 1961 - Mineola, N.Y.: Dover Publications.
    This graduate-level_text by a master in the field builds a function theory of the rational field that combines aspects of classical and intuitionist analysis. Topics include recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.
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  10.  19
    Computable Analysis.R. L. Goodstein - 1971 - Journal of Symbolic Logic 36 (1):148-150.
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  11.  40
    Transfinite ordinals in recursive number theory.R. L. Goodstein - 1947 - Journal of Symbolic Logic 12 (4):123-129.
  12.  32
    Elements of Mathematical Logic.Gert H. Muller, P. S. Novikov, Leo F. Boron & R. L. Goodstein - 1964 - Journal of Symbolic Logic 31 (4):672.
  13. The recursive irrationality of π.R. L. Goodstein - 1954 - Journal of Symbolic Logic 19 (4):267-274.
  14.  17
    Can the Logic of Indirect Discourse be Formalised?L. Jonathan Cohen, A. N. Prior & R. L. Goodstein - 1967 - Journal of Symbolic Logic 32 (4):549-550.
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  15.  23
    Empiricism in mathematics.R. L. Goodstein - 1969 - Dialectica 23 (1):50-57.
  16.  16
    Logic-free Formalisations of Recursive Arithmetic.R. L. Goodstein - 1959 - Journal of Symbolic Logic 24 (3):245-246.
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  17.  14
    Ludwig Wittgenstein und der Wiener kreis.R. L. Goodstein - 1969 - Philosophical Books 10 (1):27-28.
  18.  62
    Mathematical systems.R. L. Goodstein - 1939 - Mind 48 (189):58-73.
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  19.  14
    On formally undecidable propositions of principia mathematica and related systems.R. L. Goodstein - 1963 - Philosophical Books 4 (1):17-18.
  20.  6
    Critical notices.R. L. Goodstein - 1957 - Mind 66 (264):549-553.
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  21.  13
    Development of Mathematical Logic.J. van Heijenoort & R. L. Goodstein - 1973 - Philosophical Review 82 (3):409.
  22.  28
    A Decidable Class of Equations in Recursive Arithmetic.R. L. Goodstein & R. D. Lee - 1966 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 12 (1):235-239.
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  23. A Decidable Class of Equations in Recursive Arithmetic.R. L. Goodstein & R. D. Lee - 1968 - Journal of Symbolic Logic 33 (4):618-619.
     
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  24.  15
    A Decidable Fragment of Recursive Arithmetic.R. L. Goodstein - 1963 - Mathematical Logic Quarterly 9 (12‐15):199-201.
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  25.  22
    A Decidable Fragment of Recursive Arithmetic.R. L. Goodstein - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (12-15):199-201.
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  26.  18
    A problem in recursive function theory.R. L. Goodstein - 1953 - Journal of Symbolic Logic 18 (3):225-232.
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  27.  10
    Boolean Algebra.R. L. Goodstein - 2007 - New York: Courier Corporation.
    Famous for the number-theoretic first-order statement known as Goodstein's theorem, author R. L. Goodstein was also well known as a distinguished educator. With this text, he offers an elementary treatment that employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. The text begins with an informal introduction to the algebra of classes, exploring union, intersection, and complementation; the commutative, associative, and distributive laws; difference and symmetric difference; and Venn diagrams. Professor Goodstein proceeds to a detailed (...)
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  28.  10
    Gödel's proof.R. L. Goodstein - 1960 - Philosophical Books 1 (1):13-14.
  29.  11
    Mathematical logic and the foundations of mathematics.R. L. Goodstein - 1963 - Philosophical Books 4 (2):8-9.
  30.  8
    Models of Propositional Calculi in Recursive Arithmetic.R. L. Goodstein - 1963 - Journal of Symbolic Logic 28 (4):291-291.
  31. Mathematical Systems.R. L. Goodstein - 1939 - Journal of Symbolic Logic 4 (3):122-123.
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  32.  17
    On Limiting the Applications of the Uniqueness Rules in The Equation Calculus.R. Louis Goodstein - 1973 - Mathematical Logic Quarterly 19 (8‐10):115-116.
  33.  28
    On Limiting the Applications of the Uniqueness Rules in The Equation Calculus.R. Louis Goodstein - 1973 - Mathematical Logic Quarterly 19 (8-10):115-116.
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  34.  22
    On the nature of mathematical systems.R. L. Goodstein - 1958 - Dialectica 12 (3‐4):296-316.
    The crux of the dispute between formalism and intuitionism, it is held, is not whether certain entities exist or not, but how the term function shall be used in mathematics. The identification of effective definition with general recursion fails because an undefined function lies concealed beneath the requirement of a finite number of substitutions, and a fresh characterization of effective definition is sought in terms of a hierarchy of ordinal recursions.A correspondence exists between primitive recursive properties and direct proofs, of (...)
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  35.  1
    On the Nature of Mathematical Systems.R. L. Goodstein - 1962 - Journal of Symbolic Logic 27 (2):226-227.
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  36.  76
    On Von Mises' theory of probability.R. L. Goodstein - 1940 - Mind 49 (193):58-62.
  37.  15
    Philosophische grammatik.R. L. Goodstein - 1971 - Philosophical Books 12 (1):28-29.
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  38. Reply to mr fine's note.R. L. Goodstein - 1964 - British Journal for the Philosophy of Science 15 (58):141.
  39.  17
    Symposium: The Foundations of Mathematics.R. L. Goodstein & I. Lakatos - 1962 - Aristotelian Society Supplementary Volume 36:145 - 184.
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  40. Symposium: The Foundations of Mathematics.R. L. Goodstein & I. Lakatos - 1962 - Aristotelian Society Supplementary Volume 36:145-184.
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  41. The Axiomatic Method.R. L. Goodstein - 1962 - Aristotelian Society Supplementary Volume 36:145--54.
     
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  42.  14
    The Foundations of Mathematics.R. L. Goodstein & I. Lakatos - 1962 - Aristotelian Society Supplementary Volume 36 (1):145-184.
  43.  15
    The Mathematical Association Library at the University of Leicester.R. L. Goodstein - 1974 - British Journal for the History of Science 7 (1):100-103.
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  44.  5
    Transfinite Ordinals in Recursive Number Theory.R. L. Goodstein - 1948 - Journal of Symbolic Logic 13 (3):171-171.
  45.  1
    The philosophy of mathematics.R. L. Goodstein - 1961 - Philosophical Books 2 (1):8-9.
  46.  2
    The Recursive Irrationality of π.R. L. Goodstein - 1960 - Journal of Symbolic Logic 25 (2):166-167.
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  47.  8
    Truth Tables.R. L. Goodstein - 1973 - Journal of Symbolic Logic 38 (1):149-149.
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  48.  17
    A new proof of completeness.R. L. Goodstein - 1972 - Notre Dame Journal of Formal Logic 13 (4):563-564.
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  49.  22
    On recursive transcendence.R. L. Goodstein & J. Hooley - 1960 - Notre Dame Journal of Formal Logic 1 (4):127-137.
  50.  12
    Polynomials with computable coefficients.R. L. Goodstein - 1970 - Notre Dame Journal of Formal Logic 11 (4):447-448.
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