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Systems of predicative analysis, II: Representations of ordinals

Published online by Cambridge University Press:  12 March 2014

Solomon Feferman*
Affiliation:
Stanford University

Extract

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1968

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References

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