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Cardinality quantifiers in MLO over trees

Abstract:

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...

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Publisher:
In Proceedings of the 18th Annual Conference of the European Association for Computer Science Logic‚ CSL '09.
Volume:
5771
Publication date:
2009-01-01
URN:
uuid:79c7c897-9463-4b69-99ec-dee5376f50ba
Local pid:
cs:3168

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