Ils l'apprennent à l'école...

"Note 1.7 There is a different approach to nonstandard analysis, based on owrk by Nelson (Nelson, 1977), and known as "internal set theory", or IST. A new unary relation is first defined, a predicate to label "standard" objects, and then internal and external entities.
The axioms of IST are the usual axioms of Zermelo-Fraenkel theory with three additional ones, "transfer", "idealization", "standardization". This approach has been much developed by French mathematicians; see (Deledicq and Diener, 1989; Diener and Reeb, 1989; Lutz and Goze, 1981). It is remarkable how they have been able to transform these axioms into very hard analysis in a few pages (grifo nosso)."

(Optimization and Nonstandard Analysis, J. E. Rubio)

PS: não, eu não entendo dessas coisas, simplesmente pego livros obscuros para ler durante as aulas numa vã tentativa de ficar acordado e ocupar melhor o tempo.