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A cardinality version of Beigel's nonspeedup theorem

Published online by Cambridge University Press:  12 March 2014

James C. Owings Jr.
James C. Owings Jr.*
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742 University of Newcastle, Newcastle, New South Wales 2308, Australia
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Abstract

If S is a finite set, let ∣S∣ be the cardinality of S. We show that if m ∈ ω, A ⊆ ω, B ⊆ ω, and ∣i: ≤ i ≤ 2m & xi ∈ A}∣ can be computed by an algorithm which, for all x1, …, x2m, makes at most m queries to B, then A is recursive in the halting set K. If m = 1, we show that A is recursive.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 3 , September 1989 , pp. 761 - 767
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

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