Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-29T08:27:44.386Z Has data issue: false hasContentIssue false

Isols and the pigeonhole principle

Published online by Cambridge University Press:  12 March 2014

J. C. E. Dekker
Affiliation:
Institute for Advanced Study, Princeton, New Jersey 08540 University of California, Berkeley, California 94720 Rutgers University, New Brunswick, New Jersey 08903
E. Ellentuck
Affiliation:
Institute for Advanced Study, Princeton, New Jersey 08540 University of California, Berkeley, California 94720 Rutgers University, New Brunswick, New Jersey 08903

Abstract

In this paper we generalize the pigeonhole principle by using isols as our fundamental counting tool.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Applebaum, C. H., A stronger definition of a recursively infinite set, Notre Dame Journal of Formal Logic, vol. 14 (1973), pp. 411412.CrossRefGoogle Scholar
[2]Dekker, J. C. E., Regressive isols, Sets, models and recursion theory (Crossley, J. N., editor), North-Holland, Amsterdam, 1967, pp. 272296.CrossRefGoogle Scholar
[3]Dekker, J. C. E., Isolated sets and parity, Ciencia y Tecnologia, Revista de la Universidad de Costa Rica, vol. 8 (1984), pp. 7790.Google Scholar
[4]Dekker, J. C. E. and Ellentuck, E., Recursion relative to regressive functions, Annals of Mathematical Logic, vol. 6 (1974), pp. 231257.CrossRefGoogle Scholar
[5]Dekker, J. C. E. and Myhill, J., Recursive equivalence types, University of California Publications in Mathematics (N.S.), vol. 3 (1960), pp. 67214.Google Scholar
[6]McLaughlin, T. G., Regressive sets and the theory of isols, Marcel Dekker, New York, 1982.Google Scholar
[7]Nerode, A., Extensions to isols, Annals of Mathematics, ser. 2, vol. 73 (1961), pp. 362403.CrossRefGoogle Scholar