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Computability and Logic George S. Boolos, John P. Burgess, Richard C. Jeffrey
Publisher: Cambridge University Press

Abstract: Computability theory, which investigates computable functions and computable sets, lies at the foundation of logic and computer science. Symbolic Logic}, FJOURNAL = {The Journal of Symbolic Logic}, VOLUME = {65}, YEAR = {2000}, NUMBER = {2}, PAGES = {567--604}, We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. For the statements (7)-(11) above will all be found in various mathematics textbooks (called, e.g., A Mathematical Introduction to Logic, Computability and Logic, and so on), used in mathematics courses. I'll be teaching logic to graduate students in philosophy this coming semester. @article {HamkinsLewis2000:InfiniteTimeTM, AUTHOR = {Hamkins, Joel David and Lewis, Andy}, TITLE = {Infinite time {T}uring machines}, JOURNAL = {J. Its classical presentations usually involve a fair amount of Goedel encodings. Jeffrey Publisher: Cambridge University Press. There is a difference of emphasis, however. I sat in Soare's class in the hope some of the techniques in computability would help my research in complexity (for the most part they haven't) and have gone to a few logic seminars. Jerome Keisler et al.'s (1996) Mathematical Logic and Computability. Everything I do they call "zero.". The study of computability theory in computer science is closely related to the study of computability in mathematical logic. This page intentionally left blankComputability and Logic, Fourth EditionThis fourth edition of one of the classic logic textbooks has been thoroughly revised by JohnBurgess.