Erratum to ``What's so special about Kruskal's theorem and the ordinal \(\Gamma_0\)? A survey of some results in proof theory'' (Q1377628)

[Concerns the author's paper, ibid. 53, No. 3, 199-260 (1991; Zbl 0758.03025).] According to the author, G. Nadathur found a gap in the proof of Theorem 4.5, in particular on line 11 and below, p. 208. And, here, a corrected proof is presented. The theorem in question is Kruskal's tree theorem, and reads: ``If \(\sqsubseteq\) is a wqo on \(\Sigma\), then \(\preceq\) is a wqo on \(T_\Sigma\).'' The context is well quasi-orderings (wqo) on labeled trees. \(\Sigma\) is the given set of labels, and \(T_\Sigma\) is the set of finite \(\Sigma\)-trees. \(\preceq\) is induced on \(T_\Sigma\) from \(\sqsubseteq\) on \(\Sigma\) by `homeomorphic embedding'. The precise definition is rather lengthy, and it was given on p. 207.