(Ebook) Beyond First Order Model Theory 1st Edition by José Iovino ISBN 9781032516011, 1032516011

(Ebook) Beyond First Order Model Theory 1st Edition by José Iovino ISBN 9781032516011, 1032516011

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Product details: 

ISBN 10:1032516011

ISBN 13: 9781032516011

Author: José Iovino 

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.

Table of contents: 

I. Real-Valued Structures and Applications

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

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

3. Spectral Gap and Definability — Isaac Goldbring

II. Abstract Elementary Classes and Applications
4. Lf Groups, AEC Amalgamation, Few Automorphisms — Saharon Shelah

III. Model Theory and Topology of Spaces of Functions
5. Cp-Theory for Model Theorists — Clovis Hamel and Franklin D. Tall

IV. Constructing Many Models
6. General Non-Structure Theory — Saharon Shelah

V. Model Theory of Second Order Logic
7. Model Theory of Second Order Logic — Jouko Väänänen

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Tags: José Iovino, Beyond First Order, Model Theory