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Systems of predicative analysis, II: Representations of ordinals

  • Solomon Feferman (a1)

The eventual purpose of this paper is to provide certain specific representations of ordinals and develop their basic properties as needed for the proofs of the results announced in [3]. Since the choice of these representations is really intelligible only if the general principles involved are made explicit, we devote the first half of this paper (§§1 and 2) to such questions. The entire treatment is self-contained.

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[1]Bachmann, H., Transfinite Zahlen, Springer-Verlag, Berlin, 1955, 204 pp.
[2]Crossley, J. N. and Parikh, R.. On isomorphisms of recursive well-orderings (abstract), this Journal, vol. 28 (1963), p. 308.
[3]Feferman, S., Systems of predicative analysis, this Journal, vol. 29 (1964), pp. 130.
[4]Feferman, S. and Spector, C., Incompleteness along paths in recursive progressions of theories, this Journal, vol. 27 (1962), pp. 383390.
[5]Gandy, R. O., Proof of Mostowski's conjecture, Bulletin de l'Academk Polonaise des Sciences, vol. 8 (1960), pp. 571575.
[6]Kreisel, G., Mathematical logic, pp. 95–195 in Lectures in modern mathematics, vol. III, Wiley, New York, 1965.
[7]Mitchell, B., Theory of categories, Academic Press, New York, 1965, 273 pp.
[8]Schütte, K., Beweistheorie, Springer-Verlag, Berlin, 1960, x + 355 pp.
[9]Schütte, K., Kennzeichnungen von Ordnungzahlen durch rekursiv erklärte Funktionen, Mathematische Annalen, vol. 127 (1954), pp. 1532.
[10]Schütte, K., Predicative well-orderings, pp. 279–302 in Formal systems and recursive functions, North-Holland, Amsterdam, 1965.
[11]Spector, C., Recursive well-orderings, this Journal, vol. 20 (1955), pp. 151163.
[12]Veblen, O., Continuous increasing functions of finite and transfinite ordinals, Transactions of the American Mathematical Society, vol. 9 (1908), pp. 280292.
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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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