Isols and the pigeonhole principle

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Journal of Symbolic Logic 54 (3):833-846 (1989)
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Abstract

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

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10.2307/2274745

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Review: J. C. E. Dekker, The Minimum of Two Regressive Isols. [REVIEW]Erik Ellentuck - 1967 - Journal of Symbolic Logic 32 (4):527-527.
J. C. E. Dekker and J. Myhill. Recursive equivalence types. University of California publications in mathematics, n.s. vol. 3 no. 3 , pp. 67–214. - J. C. E. Dekker. Congruences in isols with a finite modulus. Mathematische Zeitschrift, vol. 70 , pp. 113–124. - J. Myhill. Recursive equivalence types and combinatorial functions. Bulletin of the American Mathematical Society, vol. 64 , pp. 373–376. - J. C. E. Dekker. The factorial function for isols. Mathematische Zeitschrift, vol. 70 , pp. 250–262. - J. C. E. Dekker and J. Myhill. The divisibility of isols by powers of primes. Mathematische Zeitschrift, vol. 73 . pp. 127–133. - J. C. E. Dekker. An expository account of isols. Summaries of talks presented at the Summer Institute for Symbolic Logic, Cornell University, 1957, 2nd edn., Communications Research Division, Institute for Defense Analyses, Princeton, N.J., 1960, pp. 189–200. [REVIEW]Donald L. Kreider - 1960 - Journal of Symbolic Logic 25 (4):356-359.
J. C. E. Dekker. The minimum of two regressive isols. Mathematische Zeitschrift, vol. 83 , pp. 345–366.Erik Ellentuck - 1968 - Journal of Symbolic Logic 32 (4):527.
Dekker J. C. E.. Les fonctions combinatoires et les isols. Collection de logique mathématique, série A, no. 22, Gauthiers-Villars, Paris, and E. Nauwelaerts, Louvain, 1966, 79 pp. [REVIEW]Alfred B. Manaster - 1972 - Journal of Symbolic Logic 37 (2):406-406.
An induction principle and pigeonhole principles for k-finite sets.Andreas Blass - 1995 - Journal of Symbolic Logic 60 (4):1186-1193.
On hyper‐torre isols.Joseph Barback - 2006 - Mathematical Logic Quarterly 52 (4):359-361.

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Citations of this work

Myhill's work in recursion theory.J. C. E. Dekker & E. Ellentuck - 1992 - Annals of Pure and Applied Logic 56 (1-3):43-71.

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References found in this work

Recursion relative to regressive functions.J. C. E. Dekker & E. Ellentuck - 1974 - Annals of Mathematical Logic 6 (3-4):231-257.
A stronger definition of a recursively infinite set.Charles H. Applebaum - 1973 - Notre Dame Journal of Formal Logic 14 (3):411-412.

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