Model theory selected lectures from the 2021 Thematic Program Deirdre Haskell, editor

Format:

Book

Author/Creator:

Haskell, Deirdre.

Contributor:

Haskell, Deirdre, 1963- editor.

Series:

Fields Institute communications ; 2194-1564 v. 92

Fields Institute Communications 2194-1564 volume 92

Language:

English

Subjects (All):

Model theory.

Physical Description:

1 online resource

Edition:

1st ed.

Place of Publication:

Cham Springer 2026

Summary:

This book provides an entry into some the key areas of research in contemporary model theory. Model theory, a branch of mathematical logic, is an exciting and vibrant discipline. Advances in pure model theory drive applications in algebra, algebraic geometry, analysis, combinatorics and number theory. The contributing authors are leaders in the field, both senior and junior, including Anand Pillay, Zoé Chatzidakis, Gabriel Conant, Caroline Terry, Itay Kaplan, Rahim Moosa and Silvain Rideau-Kikuchi. This book introduces readers to contemporary stability theory, the model theory of finite and pseudo-finite fields, the model theory of differential fields, and the basics of simplicity theory and NSOP1 theories, which culminate in proving the symmetry of Kim-independence. Contributors give a detailed proof of a qualitative version of the Malliaris-Shelah regularity lemma for stable graphs using only basic local stability theory and an ultraproduct construction. Additionally, contributors give self-contained exposition of two cornerstones of the geometric theory of algebraically closed valued fields. The first is a description of the definable sets in the guise of an elimination of quantifiers, essentially dating back to Robinson's work. The second is a description of all interpretable set in the guise of the Haskell-Hrushovski-Macpherson elimination of imaginaries

Contents:

Introduction, Model Theory, and Stability

Notes on the Model Theory of Finite and Pseudo-Finite Fields

Pseudo-Finite Proofs of the Stable Graph Regularity Lemma

Notes on the Basics of Simple Theories and NSOP_1

Six Lectures on Model Theory and Differentia-Algebraic Geometry

Model Theory of Valued Fields

Notes:

Includes bibliographical references

Online resource; title from PDF title page (SpringerLink, viewed May 20, 2026)

Other Format:

Print version Haskell, Deirdre Model Theory

ISBN:

9783032150233

303215023X

OCLC:

1592130905

Access Restriction:

Restricted for use by site license