Author: Salma Kuhlmann
Publisher: American Mathematical Soc.
ISBN: 0821809431
Category : Mathematics
Languages : en
Pages : 186
Get Book Here
Book Description
Model theoretic algebra has witnessed remarkable progress in the last few years. It has found profound applications in other areas of mathematics, notably in algebraic geometry and in singularity theory. Since Wilkie's results on the o-minimality of the expansion of the reals by the exponential function, and most recently even by all Pfaffian functions, the study of o-minimal expansions of the reals has become a fascinating topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a direction to this research. Through the Artin-Schreier Theory of real closed fields, the structure of the non-archimedean models in the semi-algebraic case is well understood. For the o-minimal case, so far there has been no systematic study of the non-archimedean models. The goal of this monograph is to serve this purpose. The author presents a detailed description of the non-archimedean models of the elementary theory of certain o-minimal expansions of the reals in which the exponential function is definable. The example of exponential Hardy fields is worked out with particular emphasis. The basic tool is valuation theory, and a sufficient amount of background material on orderings and valuations is presented for the convenience of the reader.
Author: Bernd Ingo Dahn
Publisher:
ISBN:
Category :
Languages : de
Pages : 14
Get Book Here
Book Description
Author: Harold G. Dales
Publisher: Oxford University Press
ISBN: 9780198539919
Category : Mathematics
Languages : en
Pages : 378
Get Book Here
Book Description
Super-fields are a class of totally ordered fields that are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are an important topic in their own right and have many surprising applications in analysis and logic. The authors introduce these exciting new fields to mathematicians, analysts, and logicians, including a natural generalization of the real line R, and resolve a number of open problems. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kapansky's embedding, they establish important new results in Banach algebra theory, non-standard analysis, and model theory.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: H. M. Fried
Publisher: Cambridge University Press
ISBN: 1139433059
Category : Science
Languages : en
Pages : 183
Get Book Here
Book Description
This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.
Author: Fabrizio Broglia
Publisher: American Mathematical Soc.
ISBN: 1470429667
Category : Mathematics
Languages : en
Pages : 390
Get Book Here
Book Description
Contains the proceedings of the international conference "Ordered Algebraic Structures and Related Topics", held in October 2015, at CIRM, Luminy, Marseilles. Papers cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.
Author: Charles N. Delzell
Publisher: American Mathematical Soc.
ISBN: 0821808044
Category : Mathematics
Languages : en
Pages : 320
Get Book Here
Book Description
This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.
Author: H. Salzmann
Publisher: Cambridge University Press
ISBN: 0521865166
Category : Mathematics
Languages : en
Pages : 418
Get Book Here
Book Description
The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.
Author: Bharath Sriraman
Publisher: Springer Nature
ISBN: 3031408462
Category :
Languages : en
Pages : 3221
Get Book Here
Book Description
Author: Pierre Ramond
Publisher: Routledge
ISBN: 0429689012
Category : Social Science
Languages : en
Pages : 345
Get Book Here
Book Description
Presents recent advances of perturbative relativistic field theory in a pedagogical and straightforward way. For graduate students who intend to specialize in high-energy physics.
