Number Theoretic Density and Logical Limit Laws (Mathematical Surveys and Monographs) - Image 1

£82.50

Brand: American Mathematical Society Number Theoretic Density and Logical Limit Laws (Mathematical Surveys and Monographs)

Name: Number Theoretic Density and Logical Limit Laws (Mathematical Surveys and Monographs)
Brand: Brand: American Mathematical Society
Price: 82.5 GBP
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Combinatorics & Graph Theory

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Description

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.

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Brand: Brand: American Mathematical Society
Format: Hardcover
ASIN: 0821826662
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Combinatorics & Graph Theory
Domain: Amazon UK
Release Date: 11 January 2001
Listed Since: 17 October 2006

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Brand: American Mathematical Society Number Theoretic Density and Logical Limit Laws (Mathematical Surveys and Monographs)

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