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Linearly stratified models for the foundations of nonstandard mathematics. (English) Zbl 0891.03035

Assuming the existence of an inaccessible cardinal, the author shows that there exist models of set theory that are transitive full and possess a linearly valued rank function. It is then shown that such models provide a global framework for nonstandard mathematics.

MSC:

03H99 Nonstandard models
03C20 Ultraproducts and related constructions
03C62 Models of arithmetic and set theory
03E55 Large cardinals
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