Categoricity theorems and conceptions of set

Journal of Philosophical Logic 31 (2):181-196 (2002)
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Two models of second-order ZFC need not be isomorphic to each other, but at least one is isomorphic to an initial segment of the other. The situation is subtler for impure set theory, but Vann McGee has recently proved a categoricity result for second-order ZFCU plus the axiom that the urelements form a set. Two models of this theory with the same universe of discourse need not be isomorphic to each other, but the pure sets of one are isomorphic to the pure sets of the other. This paper argues that similar results obtain for considerably weaker second-order axiomatizations of impure set theory that are in line with two different conceptions of set, the iterative conception and the limitation of size doctrine



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Gabriel Uzquiano
University of Southern California

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References found in this work

How we learn mathematical language.Vann McGee - 1997 - Philosophical Review 106 (1):35-68.
Iteration Again.George Boolos - 1989 - Philosophical Topics 17 (2):5-21.
How We Learn Mathematical Language.Vann McGee - 1997 - Philosophical Review 106 (1):35-68.
Models of second-order zermelo set theory.Gabriel Uzquiano - 1999 - Bulletin of Symbolic Logic 5 (3):289-302.

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