In paper [5] it was shown that a great part of model theory of logic with the generalized quantifier Qx = “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 Qx can be “syntactically” defined in a first order theory T. That problem was raised by Kosta Dosen when he asked if the quantifier Qx can be eliminated in Peano arithmetic. We answer that question fully in this paper.
['Žarko Mijajlović']
On the definability of the quantifier “there exist uncountably many”