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Model Theory in Algebra, Analysis and Arithmetic: A Preface

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Model Theory in Algebra, Analysis and Arithmetic

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2111))

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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.

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Notes

  1. 1.

    Piero Mangani died on April 4, 2013; the second author would like to devote this work to his memory.

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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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Authors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    Dugald Macpherson

  2. School of Science and Technology, Division of Mathematics, University of Camerino, 62032, Camerino, Italy

    Carlo Toffalori

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  1. Dugald Macpherson
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Correspondence to Dugald Macpherson .

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Macpherson, D., Toffalori, C. (2014). Model Theory in Algebra, Analysis and Arithmetic: A Preface. In: Model Theory in Algebra, Analysis and Arithmetic. Lecture Notes in Mathematics(), vol 2111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54936-6_1

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