TY - JOUR
T1 - Expressing cardinality quantifiers in monadic second-order logic over trees
AU - Bárány, Vince
AU - Kaiser, Łukasz
AU - Rabinovich, Alex
PY - 2010
Y1 - 2010
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.
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.
KW - Cantor topology
KW - cardinality quantifiers
KW - infinite trees
KW - monadic second-order logic
UR - http://www.scopus.com/inward/record.url?scp=77955940719&partnerID=8YFLogxK
U2 - 10.3233/FI-2010-260
DO - 10.3233/FI-2010-260
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:77955940719
SN - 0169-2968
VL - 100
SP - 1
EP - 17
JO - Fundamenta Informaticae
JF - Fundamenta Informaticae
IS - 1-4
ER -