Quantifiers and congruence closure

Studia Logica 62 (3):315-340 (1999)
We prove some results about the limitations of the expressive power of quantifiers on finite structures. We define the concept of a bounded quantifier and prove that every relativizing quantifier which is bounded is already first-order definable (Theorem 3.8). We weaken the concept of congruence closed (see [6]) to weakly congruence closed by restricting to congruence relations where all classes have the same size. Adapting the concept of a thin quantifier (Caicedo [1]) to the framework of finite structures, we define the concept of a meager quantifier. We show that no proper extension of first-order logic by means of meager quantifiers is weakly congruence closed (Theorem 4.9). We prove the failure of the full congruence closure property for logics which extend first-order logic by means of meager quantifiers, arbitrary monadic quantifiers, and the Härtig quantifier (Theorem 6.1).
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
DOI 10.1023/A:1005190726000
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 15,904
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Jouko Väänänen (1997). Unary Quantifiers on Finite Models. Journal of Logic, Language and Information 6 (3):275-304.

Monthly downloads

Added to index


Total downloads

9 ( #246,136 of 1,725,443 )

Recent downloads (6 months)

1 ( #349,420 of 1,725,443 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.