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Retraceable Sets

Published online by Cambridge University Press:  20 November 2018

J. C. E. Dekker  and
J. Myhill
J. C. E. Dekker
Affiliation:
University of California at Berkeley
J. Myhill
Affiliation:
The Institute for Advanced Study
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Let us compare two properties of sets of non-negative integers: (1) the set a has property Γ, if there exists an effective procedure which when applied to any element of a different from its maximum (which α does not necessarily possess) yields the next larger element of α; (2) the set α has property Δ, if there exists an effective procedure which when applied to any element of α different from its minimum yields the next smaller element of α. It is readily seen that every recursive set has both properties.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 357 - 373
Copyright
Copyright © Canadian Mathematical Society 1958

References

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