Abstract
Concerning the set of rooted binary trees, one shows that Higman’s Lemma and Dershowitz’s recursive path ordering can be used for the decision of its maximal order type according to the homeomorphic embedding relation as well as of the order type according to its canonical linearization, well-known in proof theory as the Feferman-Schütte notation system without terms for addition. This will be done by showing that the ordinal ω n + 1 can be found as the (maximal) order type of a set in a cumulative hierarchy of sets of rooted binary trees.
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Lee, G. (2007). Binary Trees and (Maximal) Order Types. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_48
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DOI: https://doi.org/10.1007/978-3-540-73001-9_48
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