Number Theoretic Density and Logical Limit Laws - Couverture rigide

Burris, Stanley N.

Couverture rigide

ISBN 10 : 0821826662 ISBN 13 : 9780821826669

Editeur : American Mathematical Society, 2001

Synopsis

This book shows how a study of generating series (power series in the additive case and Dirichlet series in the multiplicative case), combined with structure theorems for the finite models of a sentence, lead to general and powerful results on limit laws, including $0 - 1$ laws. The book is unique in its approach to giving a combined treatment of topics from additive as well as from multiplicative number theory, in the setting of abstract number systems, emphasizing the remarkable parallels in the two subjects.Much evidence is collected to support the thesis that local results in additive systems lift to global results in multiplicative systems. All necessary material is given to understand thoroughly the method of Compton for proving logical limit laws, including a full treatment of Ehrenfeucht-Fraisse games, the Feferman-Vaught Theorem, and Skolem's quantifier elimination for finite Boolean algebras. An intriguing aspect of the book is to see so many interesting tools from elementary mathematics pull together to answer the question: What is the probability that a randomly chosen structure has a given property? Prerequisites are undergraduate analysis and some exposure to abstract systems.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2001
• Langue: anglais
• ISBN 10: 0821826662
• ISBN 13: 9780821826669
• Reliure: Relié
• Nombre de pages: 312
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible