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Recursive equivalence types and groups1

Published online by Cambridge University Press:  12 March 2014

Matthew J. Hassett
Matthew J. Hassett*
Affiliation:
Arizona State University
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Extract

Let ε and Λ denote the sets of all nonnegative integers and isols respectively. Let σ be any subset of ε. Following [6], we shall denote the recursive equivalence type of a by Req(σ) and write σ≃τ when Req(σ) = Req(τ).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 1 , 29 May 1969 , pp. 13 - 20
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

The results presented in this paper were taken from the author's doctoral dissertation written at Rutger's—The State University under the direction of Professor J. C. E. Dekker.

References

[1]Dekker, J. C. E., The factorial function for isols, Mathematische Zeitschrift, vol. 70 (1958), pp. 250–262.CrossRefGoogle Scholar
[2]Dekker, J. C. E., Good choice sets, Annali della Scuola Normale Superiore di Pisa, vol. 20 (1966), pp. 367–393.Google Scholar
[3]Dekker, J. C. E., Infinite series of isols, Proceedings of the Symposium on Recursive Function Theory, Amer. Math. Soc., Providence, R.I., 1962, pp. 77–96.CrossRefGoogle Scholar
[4]Dekker, J. C. E., Les fonctions combinatoires et les isols, Gauthier-Villars, Paris, 1966.Google Scholar
[5]Dekker, J. C. E., The recursive equivalence type of a class of sets, Bulletin of the American Mathematical Society, vol. 70 (1964), pp. 628–632.CrossRefGoogle Scholar
[6]Dekker, J. C. E. and Myhill, J., Recursive equivalence types, University of California Publications in Mathematics (N.S.), vol. 3 (1960), pp. 67–214.Google Scholar
[7]Hall, Marshall, The theory of groups, Macmillan, New York, 1959.Google Scholar
[8]Myhill, J., Recursive equivalence types and combinatorial functions, Bulletin of the American Mathematical Society, vol. 64 (1958), pp. 373–376.CrossRefGoogle Scholar
[9]Nerode, A., Extensions to isols, Annals of Mathematics, vol. 73 (1961), pp. 362–403.CrossRefGoogle Scholar