Beyond First Order Model Theory, Volume II

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. Features 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 IovinoChapter 2. Model Theory for Real-Valued Structures H. Jerome KeislerChapter 3. Spectral Gap and Definability Isaac GoldbringII. Abstract Elementary Classes and Applications Chapter 4. Lf Groups, AEC Amalgamation, Few Automorphisms Saharon ShelahIII. Model Theory and Topology of Spaces of Functions Chapter 5. Cp-Theory for Model Theorists Clovis Hamel and Franklin D. TallIV. Constructing Many Models Chapter 6. General Non-Structure Theory. Saharon ShelahV. 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).