Decidable Expansions of Labelled Linear Orderings
Alexis Bes (University of Paris-Est Cr\'eteil), Alexander Rabinovich, (Tel-Aviv University, The Blavatnik School of Computer Science)

TL;DR
This paper explores conditions under which expanding a linear ordering with additional monadic predicates preserves decidability, focusing on structures with specific infinite intervals.
Contribution
It demonstrates that for certain linear orderings with infinite intervals, non-trivial monadic expansions can still maintain decidability of their theories.
Findings
Decidable expansions exist for linear orderings with or - type intervals.
Adding a new monadic predicate can preserve decidability under specific conditions.
The results identify when expansions do not compromise the decidability of the structure.
Abstract
Consider a linear ordering equipped with a finite sequence of monadic predicates. If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists a non-trivial expansion by a further monadic predicate that is still decidable.
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