On maximal order type of the lexicographic product
Abstract
In the previously submitted version of this paper, available here for the record, we stated the following : "We give a self-contained proof of Isa Vialard's formula for where and are wpos. The proof introduces the notion of a cut of partial order, which might be of independent interest." In fact, the argument presented in the paper is wrong and Vialard formula has no known proof. I will try to prove the formula from the [DzSS] paper because I believe that Altman's purported counter-example mentioned in the preprint is incorrect. This statement is written by Mirna D\v{z}amonja without consultation with Isa Vialard, who may hold different views. Mirna D\v{z}amonja has withdrawn her authorship from the conditionally accepted version of this note (IGPL) on January 20, 2025
Keywords
Cite
@article{arxiv.2409.09699,
title = {On maximal order type of the lexicographic product},
author = {Mirna Džamonja and Isa Vialard},
journal= {arXiv preprint arXiv:2409.09699},
year = {2025}
}
Comments
An incorrect attribution to Abraham and Bonnet of the formula $o(P\cdot Q)=o(P)\cdot o(Q)$ was given in arxiv.org/abs/1711.00428 in MATH/LO