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Solution to a Problem of Spector
- Source :
- Canadian Journal of Mathematics. 23:247-256
- Publication Year :
- 1971
- Publisher :
- Canadian Mathematical Society, 1971.
-
Abstract
- 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 thatWe 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.
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 23
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........fc25504ef2dbe95bc41356f7f1b1a7e9