Ordered Algebraic Structures and Related Topics.

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 -- References -- Stability index of algebras with involution -- 1. Introduction -- 2. Notation -- 3. Signatures revisited -- 4. Stability index of algebras with involution -- References -- Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets -- 1. Introduction -- 2. Mathematical preliminaries -- 3. Equivariant deformation -- 4. Algorithms and the proofs of the main theorems -- 5. Appendix -- References -- Gram spectrahedra -- Introduction -- 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 -- References -- 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 -- References -- 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 -- References -- Witt equivalence of fields: A survey with a special emphasis on applications of hyperfields -- 1. Introduction -- 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 -- References -- Infinite dimensional moment problem: open questions and applications -- Introduction -- 1. Preliminaries -- 2. The moment problem on lmc topological \RR-algebras -- 3. The moment problem on symmetric algebras of lc real spaces -- Acknowledgments -- References -- 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 -- References -- Coincidence point theorems for ball spaces and their applications -- 1. Introduction -- 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 -- References -- Valuation theory of exponential Hardy fields II: Principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals -- 1. Introduction -- 2. Some preliminaries -- 3. A general structure theorem for _{\cal }( ).

4. An intrinsic version of "truncation at 0" -- 5. Applications -- References -- Théories géométriques pour l'algèbre des nombres réels -- Introduction -- Introduction -- 1. Théories \gmqsz -- 2. Théories dynamiques pour les corps ordonnés -- 3. Corps ordonnés réels clos non discrets -- Conclusion -- Conclusion -- \frenchrefname -- Surreal numbers with derivation, Hardy fields and transseries: a survey -- 1. Introduction -- 2. Surreal numbers -- 3. From Hardy fields to transseries and -fields -- 4. Surreal derivations -- References -- Polynomials nonnegative on the cylinder -- Introduction -- 1. Proof of Theorem 1 -- 2. Proof of Theorem 2 -- References -- Positive semifields and their ideals -- 1. Introduction -- 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 -- References -- On the strength of some topological lattices -- 1. Introduction -- 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 -- References -- On the local geometry of definably stratified sets -- 1. Introduction -- 2. Definitions -- 3. Normal pseudo-flatness in the non-polynomially bounded case -- 4. Pawłucki's example -- References -- Back Cover.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.