Trees and nest structures

descriptionPublicationkeyboard_double_arrow_right Article 02 Sep 1966 English Publisher:Cambridge University Press (CUP)Journal:Journal of Symbolic Logic, volume 31, pages 303-321 (issn: 0022-4812, eissn: 1943-5886,

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Authors: Raymond M. Smullyan;

doi: 10.2307/2270448

Trees and nest structures

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Abstract

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.

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New School
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Keywords

mathematical logic

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