Abstract
An abstract logic,ℒ is finitely generated if it can be represented in the form ℒ ωω (Q) where Q is a finite set of Lindström quantifiers. This article is a survey of a fairly general method for proving that a given logic is not finitely generated. The main ingredients of this method are a back-and-forth charcterization of equivalence with respect to all n-ary quantifiers and constructions of non-isomorphic models for which this characterization applies.
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Hella, L., Luosto, K. (1995). Finite Generation Problem and n-ary Quantifiers. In: Krynicki, M., Mostowski, M., Szczerba, L.W. (eds) Quantifiers: Logics, Models and Computation. Synthese Library, vol 248. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0522-6_4
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