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Model Theory in Algebra, Analysis and Arithmetic: A Preface

  • Dugald Macpherson
  • Carlo Toffalori
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2111)

Abstract

Model theory is a branch of mathematical logic dealing with mathematical structures (models) from the point of view of first order logical definability. Although comparatively young, it is now well established, its major textbooks including [6, 17, 34, 43, 53]. A typical goal of model theory is to build, study and classify mathematical universes in which some given axioms (usually expressed in a first order way) are satisfied. Thus model theory has remote roots in the birth of non-Euclidean geometries and in the effort to realize them in suitable mathematical settings where their revolutionary (non-standard) assumptions are obeyed. Some major achievements of mathematical logic in the first half of the twentieth century, such as the Gödel Compactness Theorem around 1930, underpin modern model theory.

Keywords

Model Theory Independence Property Quantifier Elimination Definable Subset Exponential Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We thank the four authors of the articles in this volume for their contributions. We also warmly thank

• the CIME director and vice-director, Pietro Zecca and Elvira Mascolo, and the whole CIME staff for the excellent organization of the course,

• all the speakers, and presenters of posters,

• all the participants (around 70, mostly young researchers),

• the Italian FIR New trends in model theory of exponentiation and its coordinator Sonia L’Innocente for their support.

We also thank the CIME Scientific Committee for accepting the proposal of this course. We hope that model theory may soon be the topic of other CIME meetings.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of MathematicsUniversity of LeedsLeedsUK
  2. 2.School of Science and Technology, Division of MathematicsUniversity of CamerinoCamerinoItaly

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