A characterization of definability of second-order generalized quantifiers with applications to non-definability

A characterization of definability of second-order generalized quantifiers with applications to non-definability

Article history: Received 14 January 2012 Received in revised form 21 February 2013 Accepted 3 February 2014 Available online 4 April 2014

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...

Lindström Quantifiers and Leaf Language Definability

We show that examinations of the expressive power of logical formulae enriched by Lindström quantifiers over ordered finite structures have a well-studied complexity-theoretic counterpart: the leaf language approach to define complexity classes. Model classes of formulae with Lindström quantifiers are nothing else than leaf language definable sets. Along the way we tighten the best up to now kn...

Definability in the Monadic Second-Order Theory of Successor