Characterizing polynomial Ramsey quantifiers

Characterizing Polynomial Ramsey Quantifiers

Ramsey quantifiers are a natural object of study not only for logic and computer science, but also for the formal semantics of natural language. Restricting attention to finite models leads to the natural question whether all Ramsey quantifiers are either polynomial-time computable or NP-hard, and whether we can give a natural characterization of the polynomial-time computable quantifiers. In t...

A Dichotomy Result for Ramsey Quantifiers

Characterizing Definability of Second-Order Generalized Quantifiers

We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier Q1 is definable in terms of another quantifier Q2, the base logic being monadic second-order logic, reduces to the question if a quantifier Q1 is definable in FO(Q2, <,+,×) for certain first-order quantifiers Q1 and Q2. We use our characterization to show new de...

On the Role of Ramsey Quantifiers in First Order Arithmetic

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Characterizing Second Order Logic with First Order Quantifiers