Geodesic
Solution to a Problem of Spector
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 247-256

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Lachlan, A. H. Solution to a Problem of Spector. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 247-256. doi: 10.4153/CJM-1971-024-7
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