It was shown by Taiclin , and independently announced by Tarski , that the elementary theory of commutative cancellation semigroups is hereditarily undecidable. In his proof Tarski exhibited a subsemigroup of 〈N, ·〉, the natural numbers with multiplication, whose theory is both hereditarily and essentially undecidable. (The details of his construction were published by V. H. Dyson .) In connection with these results, Tarski suggested to the author that it would be of interest to solve the decision problem for the theory K which consists of all elementary sentences which are true in every subalgebra (i.e. every subsemigroup) of 〈N, +〉. The object of this note is to prove that the theory K is hereditarily undecidable.