LEADER 03095nam 22004693 450 001 9910482885103321 005 20231110221915.0 010 $a3-662-22378-3 035 $a(CKB)1000000000751043 035 $a(MiAaPQ)EBC3099812 035 $a(Au-PeEL)EBL3099812 035 $a(CaPaEBR)ebr10974713 035 $a(OCoLC)934997587 035 $a(BIP)11005370 035 $a(EXLCZ)991000000000751043 100 $a20210901d1993 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRecursion theory 205 $a1st ed. 210 1$aBerlin, Heidelberg :$cSpringer,$d1993. 210 4$dİ1993. 215 $a1 online resource (89 pages) 225 1 $aLecture Notes in Logic ;$vv.1 311 08$a3-540-57093-4 327 $aLecture Notes in Logic 1 Recursion Theory -- Recursion Theory -- Copyright -- Introduction -- CONTENTS -- 1. Computability -- 2. Functions and Relations -- 3. The Basic Machine -- 4. Macros -- 5. Closure Properties -- 6. Definitions of Recursive Functions -- 7. Codes -- 8. Indices -- 9. Church's Thesis -- 10. Word Problems -- 11. Undecidable Theories -- 12. Relative Recursion -- 13. The Arithmetical Hierarchy -- 14. Recursively Enumerable Relations -- 15. Degrees -- 16. Evaluation of Degrees -- 17. Large RE Sets -- 18. Function of Reals -- 19. The Analytical Hierarchy -- 20. The Projective Hierarchy -- Suggestions for Further Reading -- Index. 330 $aThese notes originated in a one semester course given several times at Duke University. Students were generally graduate students in mathematics or computer science. They were expected to have a considerable degree of mathematical maturity. While there were no specific prerequisites, it was desirable that the student has some knowledge of elementary logic and computer programming. To appreciate some of the applications, it was desirable to have at least a slight acquaintance with some other mathematical topics, such as group theory and Borel sets. My main object was to prepare the student for studying advanced books and journal articles in recursion theory. I therefore attempted to introduce as many as possible of the topics which are of interest in contemporary research without going deeply into any of them. One topic usually treated in the course which did not make its way into these notes is complexity theory; I hope that someone more competent than I will write an introduction to this topic suitable for serious mathematicians. CONTENTS 1. Computability. . . . . . 1 2. Functions and Relations . 2 .3 3. The Basic Machine . 4. Macros ....... . . 5 5. Closure Properties . . ." 410 0$aLecture Notes in Logic 676 $a511.35 700 $aShoenfield$b Joseph R$g(Joseph Robert),$f1927-$050563 701 $aGirard$b J.-Y$01225454 701 $aLachlan$b Alistair H$048457 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910482885103321 996 $aRecursion Theory$92845147 997 $aUNINA