Hilbertian fields and Hilbert's irreducibility theorem

TL;DR

This paper introduces Hilbertian fields and provides a detailed proof of Hilbert's irreducibility theorem within this framework, emphasizing its significance in inverse Galois theory.

Contribution

It formalizes the concept of Hilbertian fields and offers a comprehensive proof of Hilbert's irreducibility theorem in this setting.

Findings

Hilbertian fields are formally introduced and characterized.

A detailed proof of Hilbert's irreducibility theorem is provided.

The theorem's role in inverse Galois theory is highlighted.

Abstract

Hilbert's irreducibility theorem plays an important role in inverse Galois theory. In this article we introduce Hilbertian fields and present a clear detailed proof of Hilbert's irreducibility theorem in the context of these fields.