## Standard sets in nonstandard set theory.(English)Zbl 1067.03071

Summary: We prove that standardization fails in every nontrivial universe definable in the nonstandard set theory BST, and that a natural characterization of the standard universe is both consistent with and independent of BST. As a consequence we obtain a formulation of nonstandard class theory in the $$\in$$-language.

### MSC:

 03H05 Nonstandard models in mathematics 03E70 Nonclassical and second-order set theories

### Keywords:

nonstandard set theory BST; nonstandard class theory
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### References:

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