Regular Cost-Functions and Internal Set Theory

In this talk, I will take as an excuse regular cost-functions (an extension of regular languages with quantitative capabilities) for presenting "Internal Set Theory" (IST), an axiomatic extension of ZFC that has native non-standard analysis features. Invoking this framework yields important simplification of the proofs of cost-functions. This work, in some respect, is a continuation of ideas developed by Szymon Torunczyk during his PhD thesis.