A mathematically precise definition of the intuitive notion of "algorithm" was implicit in Kurt Godel's [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, Godel's 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.

"About this title" may belong to another edition of this title.

Store Description

Professional Book Seller offering fast shipping and hassle-free returns for every order. Our 100% satisfaction policy guarantees that you get the best product and the best service at the best price!

Visit Seller's Storefront

Seller's business information

Basi6 International LLC
1018 Camino Lago, Irving, TX, 75039, U.S.A.

Sale & Shipping Terms

Terms of Sale

Professional Book Seller shipping from Multiple Locations Worldwide for fastest delivery possible!

Shipping Terms

All orders shipped via FedEx or DHL and delivered to your doorstep within 3-5 days. We do not ship to P.O.Boxes and a proper street address must be provided to avoid any delays.

Shipping rates within U.S.A.

Shipping rates within U.S.A.
Order quantity	5 to 14 business days	3 to 6 business days
First item	US$ 0.00	US$ 0.00

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.