Composition with Algebra at the Background
Gurevich and Rabinovich raised the following question: given a property of a set of rational numbers definable in the real line by a monadic second-order formula, is it possible to define it directly in the rational line? In other words, is it true that the presence of reals at the background do not increase the expressive power of monadic second-order logic?
In this paper, we answer positively this question. The proof in itself is a simple application of classical and more recent techniques. This question will guide us in a tour of results and ideas related to monadic theories of linear orderings.
KeywordsLinear Ordering Expressive Power Regular Language Countable Word Rational Line
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