Skip Navigation

Journal of Logic and Computation 1996 6(6):779-798; doi:10.1093/logcom/6.6.779
© 1996 by Oxford University Press
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (12)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by NURMONEN, J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Original Articles

On Winning Strategies with Unary Quantifiers

JUHA NURMONEN

Department of Mathematics P.O. Box 4 (Yliopistonkatu 5) 00014 University of Helsinki Finland E-mail: juha.nurmonen{at}helsinki.fi

A combinatorial argument for two finite structures to agree on all sentences with bounded quantifier rank in first-order logic with any set of unary generalized quantifiers is given. It is known that connectivity of finite structures is neither in monadic {Sigma}11 nor in ww (Qu), where Qu is the set of all unary generalized quantifiers. Using this combinatorial argument and a combination of second-order Ehrenfeucht-Fraïssé games developed by Ajtai and Fagin, we prove that connectivity of finite structures is not in monadic {sigma}11 with any set of unary quantifiers even if sentences are allowed to contain built-in relations of moderate degree. The combinatorial argument is also used to show that no class (if it is not in some sense trivial) of finite graphs defined by forbidden minors is in ww(Qu). In particular, the class of planar graphs is not in ww(Qu)

Keywords: Ehrenfeucht-Fraissé games; finite model theory; forbidden minors; generalized quantifiers; monadic {Sigma}11


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.