Infinite Natural Numbers: an Unwanted Phenomenon, or a Useful Concept?

Abstract

We consider non-standard models of Peano arithmetic and non-standard numbers in set theory, showing that not only they appear rather naturally, but also have interesting methodological consequences and even practical applications. We also show that Czech the logical school, namely Petr Vopenka, considerably contributed to this area.

Keywords

• non-standard models
• Peano arithmetic
• non-standard analysis