The Beth-closure of l(qα) is not finitely generated

Journal of Symbolic Logic 57 (2):442 - 448 (1992)
We prove that if ℵα is uncountable and regular, then the Beth-closure of Lωω(Qα) is not a sublogic of L∞ω(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 Lindstrom quantifiers such that B(Lωω(Qα)) ≤ Lωω(Q)
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DOI 10.2307/2275278
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Lauri Hella (1989). Definability Hierarchies of Generalized Quantifiers. Annals of Pure and Applied Logic 43 (3):235-271.

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