Number Theoretic Density and Logical Limit Laws

ISBN-13: 9780821826669 / Angielski / Twarda / 2000 / 312 str.

Stanley N. Burris

Opis

This text 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. It 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-Fraiss 'e games, the Feferman-Vaught Theorem, and Skolem's quantifier elimination for finite Boolean algebras.