Abstract
In this paper we consider the problem of the definability and the eliminability of the generalized quantifier Qx= “there exist uncountably many x”. It will appear that the property of the eliminability of this quantifier is closely related to the so called regular relations, introduced in [8]. As a consequence we shall have that the significant part of model theory of logic with the quantifier Qx is reducible to the model theory of first order logic with an extra binary relation. On the other side, we can use so introduced technique to study ωl-like models of Peano arithmetic, to give alternative proofs of some two-cardinal theorems, and to prove results on end-extensions of countable models in respect to a binary relation symbol.
This work is supported by the grant 0401A of the Serbian Science Fund.
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Mijajlović, Ž. (1995). On the Eliminability of the Quantifier “There Exist Uncountably Many”. In: Krynicki, M., Mostowski, M., Szczerba, L.W. (eds) Quantifiers: Logics, Models and Computation. Synthese Library, vol 249. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0524-0_9
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DOI: https://doi.org/10.1007/978-94-017-0524-0_9
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