On the definability of the quantifier “there exist uncountably many”

Studia Logica 44 (3):257 - 264 (1985)
In paper [5] it was shown that a great part of model theory of logic with the generalized quantifier Q x = there exist uncountably many x is reducible to the model theory of first order logic with an extra binary relation symbol. In this paper we consider when the quantifier Q x can be syntactically defined in a first order theory T. That problem was raised by Kosta Doen when he asked if the quantifier Q x can be eliminated in Peano arithmetic. We answer that question fully in this paper.
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DOI 10.1007/BF00394445
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Generalized Quantification as Substructural Logic.Natasha Alechina & Michiel van Lambalgen - 1996 - Journal of Symbolic Logic 61 (3):1006 - 1044.

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