Abstract
We construct a single Lindström quantifier Q such that \(\text {FO} (Q)\), the extension of first-order logic with Q has the same expressive power as monadic second-order logic on the class of binary trees (with distinct left and right successors) and also on unranked trees with a sibling order. This resolves a conjecture by ten Cate and Segoufin. The quantifier Q is a variation of a quantifier expressing the Boolean satisfiability problem.
The research reported here was carried out while the first author was a visitor at ENS Cachan, funded by a Leverhulme Trust Study Abroad Fellowship.
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Notes
- 1.
As written in [9], the question asks for a set of such quantifiers with expressive power equivalent to \(\text {FO} (\text {MTC}) \). This is clearly a typographical error and \(\text {MSO} \) is what is meant.
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Dawar, A., Segoufin, L. (2015). Capturing MSO with One Quantifier. In: Beklemishev, L., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds) Fields of Logic and Computation II. Lecture Notes in Computer Science(), vol 9300. Springer, Cham. https://doi.org/10.1007/978-3-319-23534-9_8
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DOI: https://doi.org/10.1007/978-3-319-23534-9_8
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