Nonstandard analysis

Abstract

If one wants to present the methods of nonstandard analysis in their full generality and with full rigor, then notions and tools from mathematical logic such as “first-order formula” or “elementary extension” are definitely needed. However, we believe that a gentle introduction to the basics of nonstandard methods and their use in combinatorics does not directly require any technical machinery from logic. Only at a later stage, when advanced nonstandard techniques are applied and their use must be put on firm foundations, detailed knowledge of notions from logic will be necessary.