Frege meets zermelo: A perspective on ineffability and reflection

Review of Symbolic Logic 1 (2):241-266 (2008)
1. Philosophical background: iteration, ineffability, reflection. There are at least two heuristic motivations for the axioms of standard set theory, by which we mean, as usual, first-order Zermelo–Fraenkel set theory with the axiom of choice : the iterative conception and limitation of size . Each strand provides a rather hospitable environment for the hypothesis that the set-theoretic universe is ineffable, which is our target in this paper, although the motivation is different in each case
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DOI 10.1017/S1755020308080192
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John P. Burgess (2005). Fixing Frege. Princeton University Press.

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