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The Beth-closure of ℒ(Qα) is not finitely generated

Published online by Cambridge University Press:  12 March 2014

Lauri Hella  and
Kerkko Luosto
Lauri Hella
Affiliation:
Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland, E-mail: hella@cc.helsinki.fi
Kerkko Luosto
Affiliation:
Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland, E-maii: kluosto@cc.helsinki.fi
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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
The Journal of Symbolic Logic , Volume 57 , Issue 2 , June 1992 , pp. 442 - 448
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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