Cardinality Quantifiers in MSO on Linear Orders

Abstract

The intimate connection between first-order logic on automatic structures and MSO on (ω, < ) can be used to define generalized-automatic structures, which we introduced in section 1.5 as the ones that are MSO-to-FO interpretable in a tree. It is therefore a natural extension of the previous work to ask whether counting quantifiers preserve regularity on such generalized-automatic structures.