Nonstandard Universes

TL;DR

This paper explores the existence and fundamental properties of set-theoretic universes used in nonstandard analysis, providing an introductory overview suitable for beginners with a basic logic background.

Contribution

It offers an accessible compilation of foundational results on nonstandard universes, adapted from standard sources, for newcomers to the subject.

Findings

Existence of nonstandard universes established

Basic properties of these universes outlined

Introductory material revised for clarity

Abstract

These notes are concerned with the existence and the basic properties of the set-theoretic universes for nonstandard analysis, compiled by a beginner in the subject. It assumes a basic background in first-order logic, though the necessary material is revised in Appendix A. Needless to say, none of the material presented here is original, but has been adapted from standard sources.