Sequence system
A sequence system is an ordinal notation system in which sequences are well-ordered.
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.[1]
Notable sequence systems include Primitive sequence system, Pair sequence system, Sudden sequence system, Bashicu matrix system and Y sequence.
- ↑ Generalization of the proof of lemma 2.3 in the proof of well-foundedness of BMS