Cardinality quantifiers in MLO over trees

Vince Bárány*, Łukasz Kaiser, Alexander Rabinovich

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


We study an extension of monadic second-order logic of order with the uncountability quantifier "there exist uncountably many sets". We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over finitely branching trees, which is notable for not all of these classes are analytic. Our approach is based on Shelah's composition method and uses basic results from descriptive set theory. The elimination result is constructive, yielding a decision procedure for the extended logic. Furthermore, by the well-known correspondence between monadic second-order logic and tree automata, our findings translate to analogous results on the extension of first-order logic by cardinality quantifiers over injectively presentable Rabin-automatic structures, generalizing the work of Kuske and Lohrey.

Original languageEnglish
Title of host publicationComputer Science Logic - 23rd International Workshop, CSL 2009 - 18th Annual Conference of the EACSL, Proceedings
Number of pages15
StatePublished - 2009
Event23rd International Workshop on Computer Science Logic, CSL 2009 - 18th Annual Conference of the EACSL - Coimbra, Portugal
Duration: 7 Sep 200911 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5771 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Workshop on Computer Science Logic, CSL 2009 - 18th Annual Conference of the EACSL


FundersFunder number
Engineering and Physical Sciences Research CouncilEP/E010865/1


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