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Double Series of Isols

Published online by Cambridge University Press:  20 November 2018

Joseph Barback
Joseph Barback*
Affiliation:
The State University of New York at Buffalo
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It is assumed that the reader is familiar with the following notions: regressive function, regressive set, regressive isol, infinite series of isols, the minimum of two regressive isols, combinatorial function, and canonical extension. We shall use the slightly more general definition of a regressive function introduced in (3). The next three notions are defined in (2), the fifth in (3), and the last two in (7 and 8).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1 - 15
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Barback, J., Recursive functions and regressive isols, Math. Scand., 15 (1964), 29–42.Google Scholar
2. Dekker, J. C. E., Infinite series of isols, Proc. Symp. Recursive Function Theory (Providence, 1962), pp. 77–96.Google Scholar
3. Dekker, J. C. E., The minimum of two regressive isols, Math. Z. 83 (1964), 345–366.Google Scholar
4. Dekker, J. C. E., Les Fonctions combinatoires et les isols (Paris, 1964).Google Scholar
5. Dekker, J. C. E. and Myhill, J., Recursive equivalence types, Univ. Calif. Publ. Math. (N.S.), 3 (1960), 67–214.Google Scholar
6. Dekker, J. C. E. and Myhill, J., Retraceable sets, Can. J. Math., 10 (1958), 357–373.Google Scholar
7. Myhill, J., Recursive eqiuvalence types and combinatorial functions, (Part I), Bull. Amer. Math. Soc., 64 (1958), 373–376.Google Scholar
8. Myhill, J., Recursive equivalence types and combinatorial functions (Part 2), Proc. Symp. on Logic, Methodology and Philosophy of Science (Stanford, 1960), pp. 46–55.Google Scholar
9. Nerode, A., Extensions to isols, Ann. Math., 73 (1961), 362–403.Google Scholar
10. Nerode, A., Extensions of isolic integers, Ann. Math., 75 (1962), 419–448.Google Scholar
11. Nerode, A., Arithmetically isolated sets and nonstandard models, Proc. Symp. on Recursive Function Theory (Providence, 1962), pp. 105–116.Google Scholar
12. Sansone, F. J., Combinatorial functions and regressive isols, Pacific J. Math., 13 (1963), 703–707.Google Scholar
13. Sansone, F. J., The summation of certain infinite series of isols, Doctoral Thesis, Rutgers, The State University, 1964.Google Scholar