Van den Berg, I.P., Extended use of IST, Annals of Pure and Applied Logic 58 73–92. Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom schemes, Transfer , Idealization , and Standardization . We show that the range of application of these axiom schemes may be enlarged with respect to the original formulation. Not only more kinds of formulas are allowed, but also different settings. Many examples illustrate these extensions. Most concern formal aspects of nonstandard (...) asymptotics. (shrink)

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.