Abstract
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 Došen 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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References
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I would like to thank Kosta Došen and Zoran Marković who made valuable suggestions and remarks on a draft of this paper.
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Mijajlović, Ž. On the definability of the quantifier “there exist uncountably many”. Stud Logica 44, 257–264 (1985). https://doi.org/10.1007/BF00394445
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DOI: https://doi.org/10.1007/BF00394445