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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Constructive transfinite number classes


Author: Wayne Richter
Journal: Bull. Amer. Math. Soc. 73 (1967), 261-265
DOI: https://doi.org/10.1090/S0002-9904-1967-11710-5
MathSciNet review: 0207557
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References | Additional Information

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  • 1. J. W. Addison, Hierarchies and the axiom of constructibility, 2nd ed., Summer Institute for Symbolic Logic, Cornell University, Ithaca, N. Y., 1957, pp. 355-362, Institute for Defense Analyses, Princeton, New Jersey, 1960.
  • 2. R. O. Gandy, General recursive functionals of finite type and hierarchies of functions (mimeographed), 1962.
  • 3. S. C. Kleene, Recursive functionals and quantifiers of finite types. I, Trans. Amer. Math. Soc. 91 (1959), 1-52. MR 102480
  • 4. S. C. Kleene, Recursive functionals and quantifiers of finite types. II, Trans. Amer. Math. Soc. 108 (1963), 106-142. MR 153557
  • 5. D. L. Kreider and H. Rogers, Jr., Constructive versions of ordinal number classes, Trans. Amer. Math. Soc. 100 (1961), 325-369. MR 151396
  • 6. G. Kreisel, Review of "On hierarchies and systems of notation", Math. Reviews 28 (1964), 224.
  • 7. H. Putnam, Uniqueness ordinals in higher constructive number classes, Essays on the foundations of mathematics, The Hebrew University, Magnes Press, Jerusalem, 1961, pp. 190-206. MR 167413
  • 8. H. Putnam, On hierarchies and systems of notations, Proc. Amer. Math. Soc. 15 (1964), 44-50. MR 157898
  • 9. W. Richter, Extensions of the constructive ordinals, J. Symbolic Logic 30 (1965), 193-211. MR 219418
  • 10. J. R. Shoenfield, The form of the negation of a predicate, Recursive function theory, Proc. Sympos. Pure Math., Vol. 5, pp. 131-134, Amer. Math. Soc., Providence, R. I., 1963. MR 142449
  • 11. J. R. Shoenfield, A hierarchy for objects of type 2, Abstract 65T-173, Notices Amer. Math. Soc. 12 (1965), 369-370.
  • 12. T. Tugué, Predicates recursive in a type-2 object and Kleene hierarchies, Comment. Math. Univ. St. Paul (Tokyo) 8 (1960), 97-117. MR 110639
  • 13. Y. Suzuki, A complete classification of the Δ½-functions, Bull. Amer. Math. Soc. 70 (1964), 246-253. MR 158819


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1967-11710-5

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