Regular Languages of Words over Countable Linear Orderings

Abstract

We develop an algebraic model for recognizing languages of words indexed by countable linear orderings. This notion of recognizability is effectively equivalent to definability in monadic second-order (MSO) logic. The proofs also imply the first known collapse result for MSO logic over countable linear orderings.

Pro-aperiodic monoids via saturated models

“…In particular, it would be interesting to study the algebraic structure of Λ(A) in more detail. Here, connections with the work of Carton, Colcombet and Puppis on algebras for words over countable linear orderings [11] are to be expected.…”

Magnitude Monadic Logic over Words and the Use of Relative Internal Set Theory

“…In this paper, we do not want to be involved with infinite models. Indeed, the core of the technique deals with finite words, and treating infinite words would simply mean mixing the techniques with non immediately related notions such as Wilke algebras [23] or •-monoids [24]. This would result in many non-essential complications.…”

Recognisable Languages over Monads

“…The point of this paper is that, based on a monad one can also define things like: "syntactic algebra", "pseudovariety", "mso logic", "profinite object", and even prove some theorems about them. Furthermore, monads as an abstraction cover practically every setting where algebraic language theory has been applied so far, including labelled scattered orderings [BR12], labelled countable total orders [CCP11], ranked trees [Ste92], unranked trees [BW08], preclones [ÉW03].…”