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Trees and nest structures

1966; Cambridge University Press; Volume: 31; Issue: 3 Linguagem: Inglês

10.2307/2270448

1943-5886

Raymond M. Smullyan,

Advanced Topology and Set Theory

This paper is a sequel to [1]. Our purpose is to exhibit certain basic relationships between (ordered dyadic) trees and regular nest structures. We introduce the notion of a tree being isomorphic to a nest structure, and we study some necessary and sufficient conditions for the existence of such isomorphisms. By virtue of some of our results, Kónig's lemma on infinite trees, and our fundamental lemma of [1] concerning infinite regular nest structures become intimately related — either yields an alternative proof of the other.