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Beyond First Order Model Theory, Volume I and II book cover

1st Edition

Beyond First Order Model Theory, Volume I and II

By Jose Iovino
768 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,... Read more
Table of Contents of Volume I

I. Model Theory of Strong Logics. 1. Expressive Power of Infinitary [0, 1]-logics. 2. Scott Processes. 3. Failure of 0-1 Law for Sparse Random Graph in Strong Logics. II. Model Theory of Special Classes of Structures. 4. Maximality of Continuous Logic. 5. Model Theory and Metric Convergence I: Metastability and dominated convergence. 6. Randomizations of Scattered Sentences. 7 Existentially Closed Locally Finite Groups. 8. Analytic Zariski Structures and Non-Elementary Categoricity. III. Abstract Elementary Classes. 9. Hanf Numbers and Presentation Theorems in AECs. 10. A Survey on Tame Abstract Elementary Classes.

Table of Contents of Volume II

I. Real-Valued Structures and Applications. 1. Metastable Convergence and Logical Compactness. 2. Model Theory for Real-Valued Structures. 3. Spectral Gap and Definability. II. Abstract Elementary Classes and Applications. 4. Lf groups, AEC amalgamation, few automorphisms. III. Model Theory and Topology of Spaces of Functions. 5. Cp-Theory for Model Theorists. IV. Constructing Many Models. 6. General Non-Structure Theory. V. Model Theory of Second Order Logic. 7. Model Theory of Second Order Logic.

Biography

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).

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