Article contents
The Beth-closure of ℒ(Qα) is not finitely generated
Published online by Cambridge University Press: 12 March 2014
Abstract
We prove that if ℵα is uncountable and regular, then the Beth-closure of ℒωω(Qα) is not a sublogic of ℒαω(Qn), where Qn is the class of all n-ary generalized quantifiers. In particular, B(ℒωω(Qα)) is not a sublogic of any finitely generated logic; i.e., there does not exist a finite set Q of Lindström quantifiers such that B(ℒωω(Qα)) ≤ ℒωω(Q).
- Type
- Research Article
- Information
- Copyright
- Copyright © Association for Symbolic Logic 1992
References
REFERENCES
- 1
- Cited by