Generalizations of the one-dimensional version of the Kruskal-Friedman theorems

Publisher： Cambridge University Press

E-ISSN： 1943-5886|54|1|100-121

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.54, Iss.1, 1989-03, pp. : 100-121

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Abstract

The paper [Schütte + Simpson] deals with the following one-dimensional case of Friedman's extension (see in [Simpson 1]) of Kruskal's theorem ([Kruskal]). Given a natural number n, let S n+1 be the set of all finite sequences of natural numbers <n + 1. If s 1 = (a 0,…,ak ) ∈ S n+1 and s 2 = (b 0,…,bm ) ∈ S n + 1, then a strictly monotone function f: {0,…, k} → {0,…, m} is called an embedding of s 1 into s 2 if the following two assertions are satisfied:

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