PUTNAM, HILARY.

An Unsolvable Problem in Number Theory.

[No place], The Journal of Symbolic Logic, 1960. 8vo. In the original printed wrappers. In "Journal of Symbolic Logic", Vol. 25, Number 3, September, 1965. Previous owner's stamp (Danish philosopher Carl Henrik Koch) to top right corner of front wrapper. A very fine and clean copy. Pp. 220-232. [Entire issue: 193-304 pp.].

First printing of Putnam's influential paper in which is it documented that every recursively enumerable set is Diophantine, and hence that the set of prime numbers is Diophantine. From this, it follows that the set of prime numbers is representable by a polynomial formula. Therefore there does not exist an algorithm for
determining whether or not a polynomial (in / variables) represents every integer.

Order-nr.: 47381