Model theory of algebraically closed fields and the Ax-Grothendieck Theorem
type: CreativeWork
description: We introduce the concept of an algebraically closed field with emphasis of the basic model-theoretic results concerning the theory of algebraically closed fields. One of these nice results about algebraically closed fields is the quantifier elimination property. We also show that the theory of algebraically closed field with a given characteristic is complete and model-complete. Finally, we introduce the beautiful Ax-Grothendieck theorem and an application to it.
abstract: We introduce the concept of an algebraically closed field with emphasis of the basic model-theoretic results concerning the theory of algebraically closed fields. One of these nice results about algebraically closed fields is the quantifier elimination property. We also show that the theory of algebraically closed field with a given characteristic is complete and model-complete. Finally, we introduce the beautiful Ax-Grothendieck theorem and an application to it.
author: Elmwafy, Sayed Sayed Ahmed Osama Mohamed
keywords: Model, Structure, Quantifier Elimination, Complete, Model-complete
license: https://uwcscholar.uwc.ac.za/bitstreams/30ffe472-f89d-4ad6-ba92-3065d427d849/download
date published: 2020
date modified: 2026-07-24T06:00:42Z
provider: University of the Western Cape
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of the Western Cape