Nonstandard set theory

Journal of Symbolic Logic 54 (3):1000-1008 (1989)
Nonstandard set theory is an attempt to generalise nonstandard analysis to cover the whole of classical mathematics. Existing versions (Nelson, Hrbáček, Kawai) are unsatisfactory in that the unlimited idealisation principle conflicts with the wish to have a full theory of external sets. I re-analyse the underlying requirements of nonstandard set theory and give a new formal system, stratified nonstandard set theory, which seems to meet them better than the other versions
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DOI 10.2307/2274759
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Karel Hrbacek (2001). Realism, Nonstandard Set Theory, and Large Cardinals. Annals of Pure and Applied Logic 109 (1-2):15-48.

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