Ordered algebraic structures and related topics : International Conference on Ordered Algebraic Structures and Related Topics, October 12-16, 2015, Centre international de rencontres mathematiques (CIRM), Luminy, France / Fabrizio Broglia [and four others], editors.

Format:

Book

Conference/Event

Contributor:

Broglia, Fabrizio, 1948- editor.

Conference Name:

International Conference on Ordered Algebraic Structures and Related Topics (2015 : Marseille, France)

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 697

Contemporary mathematics, 697 0271-4132

Language:

English

Subjects (All):

Ordered algebraic structures--Congresses.

Ordered algebraic structures.

Model theory--Congresses.

Model theory.

Geometry, Algebraic--Congresses.

Geometry, Algebraic.

Forms, Quadratic--Congresses.

Forms, Quadratic.

Semigroups--Congresses.

Semigroups.

Physical Description:

1 online resource (390 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2017.

Summary:

This volume contains the proceedings of the international conference "Ordered Algebraic Structures and Related Topics", held from October 12-16, 2015, at CIRM, Luminy, Marseilles, France. Papers contained in this volume 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.

Contents:

Cover

Title page

Contents

Preface

Program of the conference

Some results on global real analytic geometry

1. Emergence of real analytic spaces

2. Inequalities and the global approach

3. Amenable -semianalytic sets and irreducible components

4. Nullstellensätze

References

Dimension in the realm of transseries

Introduction

1. Differential-algebraic dimension

2. Dimension and codimension

3. The case of \T

4. Dimension 0 = discrete

5. Parametrizability by constants

6. Dimension 0 = co-analyzable relative to the constant field

Stability index of algebras with involution

1. Introduction

2. Notation

3. Signatures revisited

4. Stability index of algebras with involution

Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets

2. Mathematical preliminaries

3. Equivariant deformation

4. Algorithms and the proofs of the main theorems

5. Appendix

Gram spectrahedra

1. Gram matrices and sums of squares

2. Connections to toric geometry

3. Ranks on Gram spectrahedra

4. Examples: Binary forms and ternary quartics

5. Hermitian Gram spectrahedra

6. Sums of squares on products of simplices

Constructions in the category of real semigroups

1. Fundamentals

2. Real semigroups of continuous functions

3. Inductive limits

4. RS-sums

5. The space of RS-characters of products of real semigroups

6. The Functor from Preordered Rings to Real Semigroups

Recent progress on definability of Henselian valuations

1. Definability of a given henselian valuation

2. Definable henselian valuations on a given henselian field

3. Quantifier complexity and questions of uniformity

Acknowledgements.

References

Polynomial, regular and Nash images of Euclidean spaces

1. First examples and obstructions

2. One dimensional polynomial and regular images of \Rⁿ

3. Examples and obstructions for dimension two

4. Obstructions for the boundaries of polynomial images

5. Piecewise linear semialgebraic sets as polynomial and regular images

6. Nash images of \Rⁿ

Witt equivalence of fields: A survey with a special emphasis on applications of hyperfields

2. Hyperfields

3. Quadratic hyperfields

4. Witt equivalence

5. Henselian valued fields

6. Local fields

7. Behaviour of orderings and valuations under Witt equivalence

8. Global fields

9. Function fields

10. Function fields over local and global fields

Infinite dimensional moment problem: open questions and applications

1. Preliminaries

2. The moment problem on lmc topological \RR-algebras

3. The moment problem on symmetric algebras of lc real spaces

Acknowledgments

A new proof for the existence of degree bounds for Putinar's Positivstellensatz

1. Introduction, definitions and historical outline of the problem

2. The purpose of the main theorem and its requirements

3. Proof of the theorem

Coincidence point theorems for ball spaces and their applications

2. Proofs of the main theorems

3. Applications to ultrametric spaces

4. An application to complete metric spaces

5. An application to ordered abelian groups and fields

6. Fixed point theorems

Valuation theory of exponential Hardy fields II: Principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals

2. Some preliminaries

3. A general structure theorem for _{\cal }( ).

4. An intrinsic version of "truncation at 0"

5. Applications

Théories géométriques pour l'algèbre des nombres réels

1. Théories \gmqsz

2. Théories dynamiques pour les corps ordonnés

3. Corps ordonnés réels clos non discrets

Conclusion

\frenchrefname

Surreal numbers with derivation, Hardy fields and transseries: a survey

2. Surreal numbers

3. From Hardy fields to transseries and -fields

4. Surreal derivations

Polynomials nonnegative on the cylinder

1. Proof of Theorem 1

2. Proof of Theorem 2

Positive semifields and their ideals

2. Definition of semifields, and examples

3. Homomorphisms

4. Ideals and factor semifields

5. The ideal spectrum of a semifield

6. Cancellation modulo ideals and the cancellation radical

7. The -kernel

8. Ideals under semifield extensions

On the strength of some topological lattices

2. The weak monadic structure of a first order structure

3. Finite unions of closed intervals

4. Defining closed and bounded intervals

5. Linear spaces and convex sets

6. Lattices of closed definable sets in the ordered context

7. Zariski closed sets and p-adic sets

8. Grzegorczyk's paper

On the local geometry of definably stratified sets

2. Definitions

3. Normal pseudo-flatness in the non-polynomially bounded case

4. Pawłucki's example

Back Cover.

Notes:

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4704-4222-1