Advances In Algebra And Model Theory
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Author | : M Droste |
Publisher | : CRC Press |
Total Pages | : 516 |
Release | : 2019-08-16 |
Genre | : Mathematics |
ISBN | : 1000725278 |
Download Advances in Algebra and Model Theory Book in PDF, Epub and Kindle
Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
Author | : Lou van den Dries |
Publisher | : Springer |
Total Pages | : 201 |
Release | : 2014-09-20 |
Genre | : Mathematics |
ISBN | : 3642549365 |
Download Model Theory in Algebra, Analysis and Arithmetic Book in PDF, Epub and Kindle
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Author | : Bradd T. Hart |
Publisher | : American Mathematical Soc. |
Total Pages | : 121 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821827057 |
Download Lectures on Algebraic Model Theory Book in PDF, Epub and Kindle
This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.
Author | : Katrin Tent |
Publisher | : Cambridge University Press |
Total Pages | : 259 |
Release | : 2012-03-08 |
Genre | : Mathematics |
ISBN | : 052176324X |
Download A Course in Model Theory Book in PDF, Epub and Kindle
Concise introduction to current topics in model theory, including simple and stable theories.
Author | : Bradd T. Hart |
Publisher | : Springer Science & Business Media |
Total Pages | : 285 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9401589232 |
Download Algebraic Model Theory Book in PDF, Epub and Kindle
Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.
Author | : Annalisa Marcja |
Publisher | : Springer Science & Business Media |
Total Pages | : 377 |
Release | : 2012-09-10 |
Genre | : Philosophy |
ISBN | : 9400708122 |
Download A Guide to Classical and Modern Model Theory Book in PDF, Epub and Kindle
This volume is easily accessible to young people and mathematicians unfamiliar with logic. It gives a terse historical picture of Model Theory and introduces the latest developments in the area. It further provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. The book is for trainees and professional model theorists, and mathematicians working in Algebra and Geometry.
Author | : Xavier Caicedo |
Publisher | : CRC Press |
Total Pages | : 474 |
Release | : 1998-11-05 |
Genre | : Mathematics |
ISBN | : 9780824719708 |
Download Models, Algebras, and Proofs Book in PDF, Epub and Kindle
"Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide."
Author | : Yi Zhang |
Publisher | : American Mathematical Soc. |
Total Pages | : 298 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 082182984X |
Download Logic and Algebra Book in PDF, Epub and Kindle
This volume outlines current developments in model theory and combinatorial set theory and presents state-of-the-art research. Well-known researchers report on their work in model theory and set theory with applications to algebra. The papers of J. Brendle and A. Blass present one of the most interesting areas of set theory. Brendle gives a very detailed and readable account of Shelah's solution for the long-standing problem of $\mathrm{Con (\mathfrak{d a )$. It could be used in anadvanced graduate seminar on set theory. Papers by T. Altinel, J. T. Baldwin, R. Grossberg, W. Hodges, T. Hyttinen, O. Lessmann, and B. Zilber deal with questions of model theory from the viewpoint of stability theory. Here, Zilber constructs an $\omega$-stable complete theory of ``pseudo-analytic''structures on algebraically closed fields. This result is part of his program of the model-theoretic study of analytic structures by including Hrushovski's method in the analytic context. The book presents this and further developments in model theory. It is geared toward advanced graduate students and researchers interested in logic and foundations, algebra, and algebraic geometry.
Author | : Philipp Rothmaler |
Publisher | : CRC Press |
Total Pages | : 324 |
Release | : 2018-12-07 |
Genre | : Mathematics |
ISBN | : 0429668503 |
Download Introduction to Model Theory Book in PDF, Epub and Kindle
Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
Author | : K. P. Shum |
Publisher | : World Scientific |
Total Pages | : 531 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9812382607 |
Download Advances in Algebra Book in PDF, Epub and Kindle
This is the proceedings of the ICM2002 Satellite Conference on Algebras. Over 175 participants attended the meeting. The opening ceremony included an address by R Gonchidorazh, former vice-president of the Mongolian Republic in Ulaanbaatar. The topics covered at the conference included general algebras, semigroups, groups, rings, hopf algebras, modules, codes, languages, automation theory, graphs, fuzzy algebras and applications.