Abstract
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
Publisher
Cambridge University Press (CUP)
Cited by
27 articles.
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