The Ax-Kochen Theorem: an application of model theory to algebra

2013/08/18 by Alex Kruckman, Kruckman, Alex · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #Polynomial and algebraic computation #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1308.3897

openalex publication_date 2013/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Ax-Kochen Theorem is a purely algebraic statement about the zeros of homogeneous polynomials over the p-adic numbers, but it was originally proved using techniques from mathematical logic. This document, the author's undergraduate honors thesis, provides an exposition of the theorem and its proof via model theory, assuming no previous experience with logic.

Cited by

• Polynomials assuming only local prime powers

Related

• The Ax-Kochen-Ershov Theorem
• Geometric proofs of theorems of Ax-Kochen and Ersov
• On Hrushovski's proof of the Manin-Mumford conjecture
• The many mathematical faces of Mermin's proof of the Kochen-Specker theorem
• Ax-Kochen-Eršov Theorems for p-adic integrals and motivic integration