Full Description
This two-volume collection contains Paulo Ribenboim's work on ordered structures and mathematical logic. Two long unpublished papers and a reproduction of his first book on abelian groups are also featured in these volumes. With over 240 publications, including 13 books, Ribenboim is responsible for some of the most influential research in number theory, mathematical logic, and algebraic structures. Together, these volumes include papers on algebraic structures on directed graphs, real algebraic geometry, applications of model theory in collaboration with Lou van dem Dries, and more recent papers with Sibylla Priess-Crampe on mathematical logic programming and Ultrametric spaces.
Originally from Brazil, Ribenboim is currently professor emeritus at Queen's University in Kingston, Ontario. The Ribenboim Prize of the Canadian Number Theory Association is named after him.
Contents
1. Characterization of the sup-complement in a distributive lattice with a last element.- 2. Conjonction d'ordres dans les groupes abeliens ordonnes.- 3. Sur les groupes totalement ordonnes et l'arithmetique des anneaux de valuation.- 4. Sur quelques constructions de groupes reticules et l'equivalence logique.- 5. Un theoreme de realisation de groupes reticules.- 6. Fonctions modulo un antifiltre.- 7. A theorem on linear transformations of torsion-free modules of infinite rank.- 8. On the existence of totally ordered abelian groups which are na-sets.- 9. A property of automorphisms of an infinite Galois extension.- 10. On ordered modules.- 11. Boolean powers.- 12. On orderable fields.- 13. On the extension of orders in ordered modules.- 14. Sur les modules ordonnes libres.- 15. Le theoreme des zeros pour les corps ordonnes.- 16. Sur le 17e probleme de Hilbert.- 17. Ronctions definies positives sur les varietes reelles.- 18. Le 17e probleme de Hilbert pour les matrices.- 19. Le 17e probleme de Hilbert.- 20. Cones in commutative algebras over ordered fields.- 21. Quelques developpements recents du 17ieme probleme Hilbert.- 22. Orders in algebras.- 23. Application de la theorie des modeles aux groupes de Galois de corps de fonctions.- 24. Vector space graphs.- 25. The algebra of functions on a graph.- 26. Algebraic structures on graphs.- 27. The absolute Galois group of a rational function field in characteristic zero is a semi-direct product.- 28. Remarks on existentially closed fields on diophantine equations.
