1st Edition

Beyond First Order Model Theory, Volume II

Edited By Jose Iovino Copyright 2023
    314 Pages 8 B/W Illustrations
    by Chapman & Hall

    314 Pages 8 B/W Illustrations
    by Chapman & Hall

    Model theory is the meta-mathematical study of the concept of mathematical truth. After Afred Tarski coined the term Theory of Models in the early 1950’s, it rapidly became one of the central most active branches of mathematical logic. In the last few decades, ideas that originated within model theory have provided powerful tools to solve problems in a variety of areas of classical mathematics, including algebra, combinatorics, geometry, number theory, and Banach space theory and operator theory.

    The two volumes of Beyond First Order Model Theory present the reader with a fairly comprehensive vista, rich in width and depth, of some of the most active areas of contemporary research in model theory beyond the realm of the classical first-order viewpoint. Each chapter is intended to serve both as an introduction to a current direction in model theory and as a presentation of results that are not available elsewhere. All the articles are written so that they can be studied independently of one another.

    This second volume contains introductions to real-valued logic and applications, abstract elementary classes and applications, interconnections between model theory and function spaces, nonstucture theory, and model theory of second-order logic.


    • A coherent introduction to current trends in model theory.
    • Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together.
    • Suitable as a reference for advanced undergraduate, postgraduates, and researchers.
    • Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature.
    • The various chapters in the book can be studied independently.

    I. Real-Valued Structures and Applications.

    Chapter 1. Metastable Convergence and Logical Compactness.
    Xavier Caicedo, Eduardo Dueñez, and José Iovino

    Chapter 2. Model Theory for Real-Valued Structures
    H. Jerome Keisler

    Chapter 3. Spectral Gap and Definability
    Isaac Goldbring

    II. Abstract Elementary Classes and Applications

    Chapter 4. Lf Groups, AEC Amalgamation, Few Automorphisms
    Saharon Shelah

    III. Model Theory and Topology of Spaces of Functions

    Chapter 5. Cp-Theory for Model Theorists
    Clovis Hamel and Franklin D. Tall

    IV. Constructing Many Models

    Chapter 6. General Non-Structure Theory.
    Saharon Shelah

    V. Model Theory of Second Order Logic

    Chapter 7. Model Theory of Second Order Logic
    Jouko Väänänen


    Jose Iovino is a professor of Mathematics at The University of Texas at San Antonio. His research is in model theory and its applications. He is the author of the monograph Applications of Model Theory to Functional Analysis (Dover Publications, 2014), a co-author of Analysis and Logic (Cambridge University Press, 2003), and the editor of the first volume of Beyond First Order Model Theory (CRC Press, 2017).