IST is more than an algorithm to prove ZFC theorems
There is a sentence in the language of IST, Nelson's internal set theory, which is not equivalent in IST to a sentence in the ∈-language. Thus the Reduction algorithm, that converts bounded IST formulas with standard parameters to provably (in IST) equivalent ∈-formulas, cannot be extended to all formulas of the IST language. Introduction. Internal set theory IST was invented by Nelson (1977) as an attempt to develop nonstandard mathematics from a unified axiomat- ical standpoint. This theory has demonstrated its ability to ground vari- ous branches of nonstandard analysis, see e.g. van den Berg (1987), F. and M.Diener (1988), F.Diener and Reeb (1989), Reeken (1992). It is regarded as one of the advantages of IST that there exists a simple algorithm, introduced also by Nelson, to transform sentences in the language of IST to provably equivalent (in the sense of provability in IST) sentences formulated in the ZFC language. This algorithm, together with Nelson's theorem that IST is a conservative extension of ZFC, is used sometimes � On leave to Bergische Universitat - Gesamthochschule Wuppertal during Spring 1993.