David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 44 (3):257 - 264 (1985)
In paper  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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References found in this work BETA
H. Jerome Keisler (1970). Logic with the Quantifier “There Exist Uncountably Many. Annals of Mathematical Logic 1 (1):1-93.
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