Note on a conjecture of Skolem
Keyword(s):
In his excellent review of four notes of Skolem on recursive functions of natural numbers Bernays states: “The question whether every relation y = f(x1,…, xn) with a recursive function ƒ is primitive recursive remains undecided.” Actually, the question is easily answered in the negative by a form of the familiar diagonal argument.We start with the ternary recursive relation R, referred to in the review, such that R(x, y, 0), R(x, y, 1), … is an enumeration of all binary primitive recursive relations.
1959 ◽
Vol 55
(2)
◽
pp. 145-148
Keyword(s):
2003 ◽
Vol 35
(103)
◽
pp. 43-68