Hyperformulas and classifications (Q2759804)

For many years, there have been various attempts to develop a complete formal syntactic approach to Nonstandard Analysis. Often any importance associated with such an approach is in the development of a ``nonstandard set-theory.'' In this paper, the authors are apparently not concerned with a nonstandard set-theory but rather approach nonstandard analysis by use of a language with infinite conjunction and disjuction. Most of the paper is the development of their hyperformula language. Using these development, the last section establishes some well-known results from elementary nonstandard analysis.