Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.   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.  ansr that question fully in this paper.
['Žarko Mijajlović']
I am writing a research paper on a idea On the definability of the quantifier “there exist uncountably many”
[{"from": "human", "value": "I am writing a research paper on a idea On the definability of the quantifier \u201cthere exist uncountably many\u201d"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In paper [5] it was shown that a great part of model theory of logic with the generalized quantifier Qx = \u201cthere exist uncountably many x\u201d is reducible to the model theory of first order logic with an extra binary relation symbol.   consider when the quantifier Qx can be \u201csyntactically\u201d 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.  ansr that question fully in this paper."}]