Ralph McKenzie; Matthew Valeriote Structure of Decidable Locally Finite Varieties 9781461289081

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Автор: Ralph McKenzie; Matthew Valeriote
Название: Structure of Decidable Locally Finite Varieties
ISBN: 9781461289081
Издательство: Springer
Классификация: ISBN-10: 1461289084
Обложка/Формат: Paperback
Страницы: 216
Вес: 0.31 кг.
Дата издания: 08.10.2011
Серия: Progress in Mathematics
Язык: English
Размер: 229 x 152 x 12
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: A mathematically precise definition of the intuitive notion of algorithm was implicit in Kurt Godels 1931] paper on formally undecidable propo- sitions of arithmetic. During the 1930s, in the work of such mathemati- cians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godels idea evolved into the concept of a recursive function. Church pro- posed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)-i. e., that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski 1949]), the theory of Abelian groups (Szmiele 1955]), and the theories of elementary arithmetic and geometry (Tarski 1951] but Tarski discovered these results around 1930). The de- termination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A.

Structure of Decidable Locally Finite Varieties, Ralph McKenzie; Matthew Valeriote