Expressing cardinality quantifiers in monadic second-order logic over trees

Vince Bárány, Łukasz Kaiser, Alex Rabinovich

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalFundamenta Informaticae
Volume100
Issue number1-4
DOIs
StatePublished - 2010

Keywords

  • Cantor topology
  • cardinality quantifiers
  • infinite trees
  • monadic second-order logic

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