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Foundations for analysis and proof theory

Synthese 60 (2):159 - 200 (1984)

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  1. Das Kontinuum.H. Weyl - 1960 - Journal of Symbolic Logic 25 (3):282-284.
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  • Functionals defined by transfinite recursion.W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):155-174.
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  • Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
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  • Abhandlungen zur Philosophie der Mathematik.G. T. Kneebone & Paul Bernays - 1977 - Philosophical Quarterly 27 (106):72.
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  • A survey of proof theory.G. Kreisel - 1968 - Journal of Symbolic Logic 33 (3):321-388.
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  • Beyond first-order logic: the historical interplay between mathematical logic and axiomatic set theory.Gregory H. Moore - 1980 - History and Philosophy of Logic 1 (1-2):95-137.
    What has been the historical relationship between set theory and logic? On the one hand, Zermelo and other mathematicians developed set theory as a Hilbert-style axiomatic system. On the other hand, set theory influenced logic by suggesting to Schröder, Löwenheim and others the use of infinitely long expressions. The questions of which logic was appropriate for set theory - first-order logic, second-order logic, or an infinitary logic - culminated in a vigorous exchange between Zermelo and Gödel around 1930.
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  • Russell's Mathematical Logic.Kurt Gödel - 1946 - In Paul Arthur Schilpp (ed.), The Philosophy of Bertrand Russell, 2nd edition. Evanston, IL: The Library of Living Philosophers, Inc.. pp. 123-154.
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  • Systems of predicative analysis.Solomon Feferman - 1964 - Journal of Symbolic Logic 29 (1):1-30.
    This paper is divided into two parts. Part I provides a resumé of the evolution of the notion of predicativity. Part II describes our own work on the subject.Part I§1. Conceptions of sets.Statements about sets lie at the heart of most modern attempts to systematize all (or, at least, all known) mathematics. Technical and philosophical discussions concerning such systematizations and the underlying conceptions have thus occupied a considerable portion of the literature on the foundations of mathematics.
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  • A more perspicuous formal system for predicativity.Solomon Feferman - 1978 - In Kuno Lorenz (ed.), Konstruktionen Versus Positionen: Beiträge Zur Diskussion Um Die Konstruktive Wissenschaftstheorie. Bd 1: Spezielle Wissenschaftstheorie. Bd 2: Allgemeine Wissenschaftstheorie. Paul Lorenzen Zum 60. Geburtstag. New York: De Gruyter. pp. 68-93.
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  • Mathematische Existenz und Widerspruchsfreiheit.Paul Bernays - 1957 - Journal of Symbolic Logic 22 (2):210-211.
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  • Die Philosophie der Mathematik und die Hilbertsche Beweistheorie.Paul Bernays - 1978 - Journal of Symbolic Logic 43 (1):148-149.
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  • Bemerkungen zu Lorenzen's stellungnahme in der philosophie der mathematik.Paul Bernays - 1978 - In Kuno Lorenz (ed.), Konstruktionen Versus Positionen: Beiträge Zur Diskussion Um Die Konstruktive Wissenschaftstheorie. Bd 1: Spezielle Wissenschaftstheorie. Bd 2: Allgemeine Wissenschaftstheorie. Paul Lorenzen Zum 60. Geburtstag. New York: De Gruyter. pp. 3-16.
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  • Two applications of logic to mathematics.Gaisi Takeuti - 1978 - [Princeton, N.J.]: Princeton University Press.
    Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that (...)
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  • Principia Mathematica Vol. I.Bertrand Russell & Alfred North Whitehead - 1910 - Cambridge University Press.
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  • Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.K. Gödel - 1931 - Monatshefte für Mathematik 38 (1):173--198.
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  • Hilbert.Constance Reid - 1999 - Studia Logica 63 (2):297-300.
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  • Hilbert.Constance Reid - 1972 - Philosophy of Science 39 (1):106-108.
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  • From Frege to Gödel.Jean van Heijenoort - 1968 - Philosophy of Science 35 (1):72-72.
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  • Trees in Metamathematics.Wilfried Sieg - 1977 - Dissertation, Stanford University
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