Expressing cardinality quantifiers in monadic second-order logic over chains

Vince Bárány, Lukasz Kaiser, Alexander Rabinovich

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the extension of monadic second-order logic of order with cardinality quantifiers "there exists uncountably many sets such that⋯" and "there exists continuum many sets such that⋯ ". We prove that over the class of countable linear orders the two quantifiers are equivalent and can be effectively and uniformly eliminated. Weaker or partial elimination results are obtained for certain wider classes of chains. In particular, we show that over the class of ordinals the uncountability quantifier can be effectively and uniformly eliminated. Our argument makes use of Shelah's composition method and Ramsey-like theorem for dense linear orders.

Original languageEnglish
Pages (from-to)603-619
Number of pages17
JournalJournal of Symbolic Logic
Volume76
Issue number2
DOIs
StatePublished - Jun 2011

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