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Solution to a Problem of Spector

Published online by Cambridge University Press:  20 November 2018

A. H. Lachlan
A. H. Lachlan*
Affiliation:
Simon Fraser University, Burnaby, British Columbia
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In [6, p. 586] Spector asked whether given a number e there exists a unary partial function from the natural numbers into {0, 1} with coinfinite domain such that for any function ƒ into {0, 1} extending it is the case that

We answer this question affirmatively in Corollary 1 below and show that can be made partial recursive (p.r.) with recursive domain. The reader who is familiar with Spector's paper [6] will find the new trick that is required in the first paragraph of the proof of Lemma 2 below.

From one point of view, this is a theorem about trees which branch twice at every node. We shall formulate a generalization which applies to trees which branch n times at every node.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 2 , April 1971 , pp. 247 - 256
Copyright
Copyright © Canadian Mathematical Society 1971

References

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