Definability hierarchies of generalized quantifiers
نویسندگان
چکیده
منابع مشابه
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...
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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...
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We show that for each n and m, there is an existential first order sentence which is NOT logically equivalent to a sentence of quantifier rank at most m in infinitary logic augmented with all generalized quantifiers of arity at most n. We use this to show the strictness of the quantifier rank hierarchies for various logics ranging from existential (or universal) fragments of first order logic t...
متن کاملA 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
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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...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1989
ISSN: 0168-0072
DOI: 10.1016/0168-0072(89)90070-5