‎Boolos George Jeffrey Richard C‎
‎Computability And Logic‎

‎Bulos D., Jeffrey R. Computability and Logic. In Russian /Bulos D., Dzheffri ‎

‎Bulos D., Jeffrey R. Computability and Logic. In Russian /Bulos D., Dzheffri R. Vychislimost i logika. Translation from English. Moscow World 1994. 396 p. We have thousands of titles and often several copies of each title may be available. Please feel free to contact us for a detailed description of the copies available. SKUalbe8ed16c9ef5e74ef.‎

‎Computability and Lambda-Definability. (Extracted from The Journal of Sybolic Logic, Volume 2, 1937, pp.153-64.).‎

‎1937. 8vo. Bound in recent marbled boards. Title-page for volume 2 of Journal of Symbolic Logic withbound.‎

‎First edition of Turing's important paper, in which he links Kleene's recursive functions, Church's lambda-definable functions and his own computable functions and proves them to be identical. In the appendix of his milestone-paper ""On Computable Numbers"" from 1936, Turing gave a short outline of a method for proving that his notion of computability is equivalent with Alonzo Church's notion of lambda-definabilty. It was not until the present article, however, that it was proved that Steven Kleene's general recursive functions, Church's lambda-definable functions and Turing's computable functions were all identical. Kleene had already proved that every general recursive function is lambda-definable, so by showing that computability follows from lambda-definability and that general recursiveness follows from computability, Turing had ended the circle, which was a primary reason for its acceptance as a notion of ""effective calculable"" demanded by Hilbert's Entscheidungsproblem.""The purpose of the present paper is to show that the computable functions introduced by the author (in ""On computable numbers"") are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene."" Turing wrote this paper while at Princeton studying with Church.""(Hook and Norman No. 395)‎

‎A First Course in Logic - An Introduction to Model Theory, Proof Theory, Computability and Complexity‎

‎Oxford University Press , Oxford Texts in Logic Malicorne sur Sarthe, 72, Pays de la Loire, France 2004 Book condition, Etat : Très Bon paperback, editor's printed and illustrated wrappers grand In-8 1 vol. - 451 pages‎

‎ 1st paperback Contents, Chapitres : Acknowledgments, Contents, Preliminaries, xx, Text, 431 pages - Propositional logic - Structures and first-order logic - Proof theory - Properties of first-order logic - First-order theories - Models of countable theories - Computability and complexity - The incompleteness theorems - Beyond first-order logic - Finite model theory - Bibliography and index Near fine copy, no markings‎

‎On the interpretation of intuitionistic number theory. - [FIRST FORMAL TREATMENTS OF LOGIC FOR COMPUTABILITY]‎

‎(No place), The Association for Symbolic Logic, 1944 & 1945. Lev8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 9 & 10 bound together. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. A very fine copy. [Kleene:] Pp. 109-124. [Entire volume: IV, 107, (1), IV, 160 pp.].‎

‎First printing of Kleene's important paper constituting one of the very first formal treatments of logic for computability in which he proved that intuitionistic first-order number theory also has the related existence property through an interpretation of intuitionistic number theory in terms of Turing machine computations.‎