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Mitotic recursively enumerable sets

Published online by Cambridge University Press:  12 March 2014

Richard E. Ladner
Richard E. Ladner*
Affiliation:
Simon Fraser University, Burnaby 2, British Columbia, Canada University of California, Berkeley, California 94720
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Extract

A recursively enumerable (r.e.) set is mitotic if it is the disjoint union of two r.e. sets both of the same degree of unsolvability. A. H. Lachlan has shown in [3] that there exists a nonmitotic r.e. set. In this paper we make an initial investigation into the class of mitotic sets.

The following results are proved, (i) An r.e. set is mitotic if and only if it is auto-reducible, (ii) There is a nonmitotic r.e. set of degree 0′, (iii) If d is an arbitrary non-recursive r.e. degree then there exists a nonmitotic r.e. set of degree ≤d. (iv) There exists a maximal set which is mitotic and a maximal set which is nonmitotic.

Albert R. Meyer had independently proved (ii) and (iii) for nonautoreducible sets before (i) was known.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 38 , Issue 2 , June 1973 , pp. 199 - 211
Copyright
Copyright © Association for Symbolic Logic 1973

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References

REFERENCES

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