Sequence system: Difference between revisions

 

Typically, it is an [[expansion system]], with the expansion chosen so that \( x[n] \) is always lexicographically smaller than \( x \), and additionally, so that \( x[0] \) is \( x \) without its last element and \( x[n] \) is always a subsequence of \( x[n+1] \). If all of these hold, then as long as the base of its standard form is totally ordered, the order of the sequence system is identical to the lexicographical order.<ref>Generalization of the proof of lemma 2.3 in the [https://arxiv.org/abs/2307.04606 proof of well-foundedness] of [[Bashicu matrix system | BMS]]</ref>