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2010

Expressing Cardinality Quantifiers in Monadic Second-Order Logic over Trees

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Expressing Cardinality Quantifiers in Monadic Second-Order Logic over Trees
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.
Vince Bárány, Lukasz Kaiser, Alexand
Added 02 Mar 2011
Updated 02 Mar 2011
Type Journal
Year 2010
Where FUIN
Authors Vince Bárány, Lukasz Kaiser, Alexander Moshe Rabinovich
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