TY - GEN
T1 - Cardinality quantifiers in MLO over trees
AU - Bárány, Vince
AU - Kaiser, Łukasz
AU - Rabinovich, Alexander
N1 - Funding Information:
This research was facilitated by the ESF project AutoMathA. The first author was supported in part by ANR-06-MDCA-05 (2007-2009) DocFlow, and by the EPSRC grant EP/E010865/1.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70350353653&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-04027-6_11
DO - 10.1007/978-3-642-04027-6_11
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AN - SCOPUS:70350353653
SN - 3642040268
SN - 9783642040269
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 117
EP - 131
BT - Computer Science Logic - 23rd International Workshop, CSL 2009 - 18th Annual Conference of the EACSL, Proceedings
T2 - 23rd International Workshop on Computer Science Logic, CSL 2009 - 18th Annual Conference of the EACSL
Y2 - 7 September 2009 through 11 September 2009
ER -