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Systems of predicative analysis1

  • Solomon Feferman (a1)

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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Text of an invited address delivered to a meeting of the Association for Symbolic Logic at Berkeley, California, on January 26, 1963.

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[1] S. Feferman , Classifications of recursive functions by means of hierarchies, Transactions of the American Mathematical Society, vol. 104 (1962), pp. 101122.

[7] S. C. Kleene , Hierarchies of number-theoretic predicates, Bulletin of the American Mathematical Society, vol. 61 (1955), pp. 193213.

[8] S. C. Kleene , On the forms of predicates in the theory of constructive ordinals, II, American journal of mathematics, vol. 77 (1955), pp. 405428.

[19] K. Schütte , Kennzeichnung von Ordnungszahlen durch rekursiv erklärte Funktionen, Mathematische Annalen, vol. 127 (1954), pp. 1532.

[20] C. Spector , Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics, Recursive function theory. Proceedings of symposia in pure mathematics (Providence), vol. 5 (1962), pp. 127.

[23] G. Takeuti , On the fundamental conjecture of GLC. VI, Proceedings of the Japan Academy, vol. 37 (1961), pp. 440443.

[24] G. Takeuti , On the inductive definition with quantifiers of second order, Journal of the Mathematical Society of Japan, vol. 13 (1961), pp. 333341.

[25] O. Veblen , Continuous increasing functions of finite and transfinite ordinals, Transactions of the American Mathematical Society, vol. 9 (1908), pp. 280292.

[26] H. Wang , A survey of mathematical logic, Amsterdam, North-Holland Publishing Company, 1963.

[27] H. Wang , Ordinal numbers and predicative set theory, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 5 (1959), pp. 216239.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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