 This simple fact about models of Peano arithmetic was not pointed out by Gödel in any of the publications connected with the Completeness Theorem from that time, and it seems not to have been noticed by the general logic community until much later. Skolem’s definable ultrapower construction from 1933 (see Skolem 1933) gives a direct construction of a non-standard model of True Arithmetic (which extends Peano arithmetic, being the set of arithmetic sentences true in the natural numbers). But Skolem never mentions the fact that the existence of such models follows from the completeness and compactness theorems. Gödel in his review (1934c) of Skolem’s paper also does not mention this fact, rather observing that the failure of categoricity for arithmetic follows from the incompleteness theorem.