First order quantifiers in monadic second order logic

First order quantifiers in~monadic second order logic

This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01]. We introduce an operation existsn(S) on properties S that says “there are n components having S”. We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to th...

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 ...

Expressing cardinality quantifiers in monadic second-order logic over chains

We study the extension of monadic second-order logic of order with cardinality quantifiers “there exists infinitely many sets” and “there exists uncountably many sets”. On linear orders that require the addition of only countably many points to be complete, we show using the composition method that the second-order uncountability quantifier can be reduced to the first-order uncountability quant...

Monadic Second Order Logic with Measure and Category Quantifiers

We investigate the extension of Monadic Second Order logic, interpreted over infinite words and trees, with generalized “for almost all” quantifiers interpreted using the notions of Baire category and Lebesgue measure. All three authors were supported by the Polish National Science Centre grant no. 2014-13/B/ST6/03595. The work of the second author has also been supported by the project ANR-16-...

Characterizing Second Order Logic with First Order Quantifiers