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Trees and nest structures

Published online by Cambridge University Press:  12 March 2014

Raymond M. Smullyan
Raymond M. Smullyan*
Affiliation:
Belfer Graduate School of Science New York, New York
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Extract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 303 - 321
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Smullyan, R. M., Analytic Natural Deduction, this Journal, vol. 30 (1965), pp. 123–139.Google Scholar
[2]Beth, E. W., The Foundations of Mathematics, North Holland Publishing Co., Amsterdam, 1959.Google Scholar
[3]Jaakko, K.Hintikka, J., Form and content in quantification theory, Acta Philosophica Fenniça No. 8, Helsinki 1955, pp. 7–55.Google Scholar
[4]Smullyan, R. M., A unifying principle in quantification theory, Proceedings of the National Academy of Sciences, vol. 49, no. 6, pp. 828–832, June 1963.CrossRefGoogle Scholar