A note on universal sets
A. H. Lachlan · Journal of Symbolic Logic · 1966
In this note is proved the following: Theorem.Iƒ A × B is universal and one oƒ A, B is r.e. then one of A, B is universal. Letα, τbe 1-argument recursive functions such thatxgoes to (σ(χ), τ(χ)) is a (1–1) map of the natural numbers onto all ordered pairs of natural numbers. A set A of natural numbers is calleduniversalif every r.e. set is (many-one) reducible to A; A × B is calleduniversalif the set