On second-order generalized quantifiers and finite structures

Definability of second order generalized quantifiers

Acknowledgements I wish to express my sincere gratitude to my supervisor Professor Jouko Väänänen for introducing me to this subject and for his inspiring guidance and support during my doctoral studies. I am also grateful to Professor Lauri Hella and Docent Kerkko Luosto for carefully reading the manuscript and making valuable comments on it. I am indebted to the Graduate School of Mathematica...

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 Second-Order Monadic Groupoidal Quantifiers

We study logics defined in terms of so-called second-order monadic groupoidal quantifiers. These are generalized quantifiers defined by groupoid word-problems or equivalently by context-free languages. We show that, over strings with built-in arithmetic, the extension of monadic second-order logic by all second-order monadic groupoidal quantifiers collapses to its fragment mon-QGrpFO. We also s...

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be ...

Characterizing Second Order Logic with First Order Quantifiers