The Recursion Theorem and Infinite Sequences

الأصل · EN

In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e₀, e₁, e₂.. such that Wₑₙ=eₙ₊₁ for every n. Similarly, we prove that there exists an increasing sequence such that Wₑₙ=eₙ₊₁,eₙ₊₂,... for every n. We call a nonempty computably enumerable set A self-constructing if Wₑ=A for every e in A. We show that every nonempty computable enumerable set which is disjoint from an infinite computable set is one-one equivalent to a self-constructing set