Limited Set quantifiers over Countable Linear Orderings

@inproceedings{Colcombet2015LimitedSQ,
  title={Limited Set quantifiers over Countable Linear Orderings},
  author={Thomas Colcombet and A. V. Sreejith},
  booktitle={ICALP},
  year={2015}
}
In this paper, we study several sublogics of monadic second-order logic over countable linear orderings, such as first-order logic, first-order logic on cuts, weak monadic second-order logic, weak monadic second-order logic with cuts, as well as fragments of monadic second-order logic in which sets have to be well ordered or scattered. We give decidable algebraic characterizations of all these logics and compare their respective expressive power. 
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References

SHOWING 1-10 OF 38 REFERENCES
Complementation of rational sets on countable scattered linear orderings
TLDR
It is proved that rational sets of words on countable scattered linear orderings are closed under complementation using an algebraic approach.
Regular Languages of Words over Countable Linear Orderings
TLDR
An algebraic model for recognizing languages of words indexed by countable linear orderings that is effectively equivalent to definability in monadic second-order (MSO) logic is developed.
Algebraic Characterization of FO for Scattered Linear Orderings
We prove that for the class of sets of words indexed by countable scattered linear orderings, there is an equivalence between definability in first-order logic, star-free expressions with marked
LINEAR ORDERINGS
The monadic theory of order
TLDR
It is proved that the monadic theory of the real order is undecidable, which means that all known results in a unified way are proved.
Definability and undefinability with real order at the background
TLDR
It is reasonable to expect that the presence of a background chain allows one to define point sets (or families of point-sets) on A which are not definable inside .
Decidability of second-order theories and automata on infinite trees
Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involves
Decidability of second-order theories and automata on infinite trees.
Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involves
De nability and Unde nability with Real Order at the Background
A formula (X) with one free monadic predicate variable de nes the set of predicates (or family of point-sets) on A that satisfy (X). This family is said to be de nable by (X) in A: Suppose that A is
An Algebraic Theory for Regular Languages of Finite and Infinite Words
  • T. Wilke
  • Mathematics
    Int. J. Algebra Comput.
  • 1993
TLDR
An algebraic approach to the theory of regular languages of finite and infinite words (∞-languages) is presented and a variety theorem is proved: there is a one-to-one correspondence between varieties of ∞-Languages and pseudovarieties of right binoids.
...
...