BU CLA MA 531 : Computability and Logic Handout 5 Assaf
نویسنده
چکیده
Proof: Using induction, we define an infinite sequence of nodes x0, x1, . . ., forming an infinite path in T . At stage 0 of the induction, let x0 be the root of T , which has infinitely many successors by the hypothesis that T is infinite. At stage n ≥ 1, assume we have already selected nodes x0, x1, . . . , xn−1 so far, forming a path of length n−1, such that xn−1 has infinitely many successors. By hypothesis, T is finitely branching, which implies xn−1 has only finitely many immediate successors. Hence, one of the immediate successors of xn−1, say y, must have infinitely many successors. Define xn to be y, which has infinitely many successors in T , and proceed to stage n + 1 of the induction.
منابع مشابه
BU CLA MA 531 : Computability and Logic
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