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 ...
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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.
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Add this copy of Structure of Decidable Locally Finite Varieties to cart. $60.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2011 by Birkhauser.
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Near Fine. Boston: Birkhauser, 1989. viii, 212 pp. 23.5 x 15.5 cm. Glossy paper covered boards printed dark green with white lettering. Very light rubbing to covers consistent with minimal shelfwear. Interior is clean and unmarked. Binding firm. Hard Cover. Near Fine.
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Good. Ex-library copy with stamps and stickers. The copy shows minor external wear, but is in otherwise clean condition. Very Clean Copy-Over 500, 000 Internet Orders Filled.
Add this copy of Structure of Decidable Locally Finite Varieties to cart. $60.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1989 by Birkhauser.
Add this copy of Structure of Decidable Locally Finite Varieties to cart. $64.39, new condition, Sold by Basi6 International rated 5.0 out of 5 stars, ships from Irving, TX, UNITED STATES, published 1989 by Birkhauser.
Add this copy of Structure of Decidable Locally Finite Varieties to cart. $65.00, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1989 by Birkhäuser.
