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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 Two long unpublished papers and a reproduction of his first book on abelian groups are also featured in these volumes.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 den Dries, and more recent papers with Sibylla Priess-Crampe on mathematical logic programming and Ultrametric spaces. The Ribenboim Prize of the Canadian Number Theory Association is named after him. Paulo Ribenboim is currently professor emeritus at Queen's University in Kingston, Ontario.
List of contents
30. Equivalent forms of Hensel's lemma.- 31. Il Mondo Krasneriano.- 32. The ascending chain condition of real ideals.- 33. An application of Tarski's principle to absolute Galois groups of function fields, I.- 34. An application of Tarski's principle to absolute Galois groups of function fields, II.- 35. Commutative convolution rings of ordered monoids.- 36. Generalized power series rings.- 37. Fields of generalized power series.- 38. Fields: Algebraically closed and others zed power series.- 39. Fixed points, combs and generalized power series.- 40. Ordered rings of generalized power series.- 41. Some examples of lattice-orders in real closed fields.- 42. Chaining partially ordered sets.- 43. Automorphisms of the ordered multiplicative group of positive rational numbers.- 44. Some examples of valued fields.- 45. On Rolle fields, with examples.- 46. Ordering the set of antichains of an ordered set.- 47. Ultrametric spaces and logic programming.- 48. Response.
About the author
Well known for his contributions in number theory, Paulo Ribenboim has authored over 240 publications, including 13 books. He is now professor emeritus at Queen’s University in Kingston, Ontario. The Ribenboim Prize of the Canadian Number Theory Association is named after him.
Summary
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 Two long unpublished papers and a reproduction of his first book on abelian groups are also featured in these volumes.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 den Dries, and more recent papers with Sibylla Priess-Crampe on mathematical logic programming and Ultrametric spaces. The Ribenboim Prize of the Canadian Number Theory Association is named after him. Paulo Ribenboim is currently professor emeritus at Queen’s University in Kingston, Ontario.
