Expressing Cardinality Quantifiers in Monadic Second-Order Logic over Trees
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 …