LEADER 03636nam 2200589 450 001 9910827106603321 005 20211025123824.0 010 $a3-662-11686-3 024 7 $a10.1007/978-3-662-11686-9 035 $a(CKB)2660000000028566 035 $a(SSID)ssj0001296582 035 $a(PQKBManifestationID)11775212 035 $a(PQKBTitleCode)TC0001296582 035 $a(PQKBWorkID)11353067 035 $a(PQKB)10188923 035 $a(DE-He213)978-3-662-11686-9 035 $a(MiAaPQ)EBC3100324 035 $a(MiAaPQ)EBC6555597 035 $a(Au-PeEL)EBL6555597 035 $a(OCoLC)1255234479 035 $a(PPN)237949105 035 $a(EXLCZ)992660000000028566 100 $a20211025d1965 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aEnumerability, decidability, computability $ean introduction to the theory of recursive functions /$fHans Hermes ; Translated by Gabor T. Herman and O. Plassmann 205 $a1st ed. 1965. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1965] 210 4$dİ1965 215 $a1 online resource (X, 245 p.) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v127 300 $aIncludes index. 311 $a3-662-11688-X 327 $a1. Introductory Reflections on Algorithms -- 2. Turing Machines -- 3. ?-Recursive Functions -- 4. The Equivalence of Turing-Computability and?-Recursiveness -- 5. Recursive Functions -- 6. Undecidable Predicates -- 7. Miscellaneous -- Author and Subject Index. 330 $aThe task of developing algorithms to solve problems has always been considered by mathematicians to be an especially interesting and im­ portant one. Normally an algorithm is applicable only to a narrowly limited group of problems. Such is for instance the Euclidean algorithm, which determines the greatest common divisor of two numbers, or the well-known procedure which is used to obtain the square root of a natural number in decimal notation. The more important these special algorithms are, all the more desirable it seems to have algorithms of a greater range of applicability at one's disposal. Throughout the centuries, attempts to provide algorithms applicable as widely as possible were rather unsuc­ cessful. It was only in the second half of the last century that the first appreciable advance took place. Namely, an important group of the inferences of the logic of predicates was given in the form of a calculus. (Here the Boolean algebra played an essential pioneer role. ) One could now perhaps have conjectured that all mathematical problems are solvable by algorithms. However, well-known, yet unsolved problems (problems like the word problem of group theory or Hilbert's tenth problem, which considers the question of solvability of Diophantine equations) were warnings to be careful. Nevertheless, the impulse had been given to search for the essence of algorithms. Leibniz already had inquired into this problem, but without success. 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v127 606 $aMathematics 615 0$aMathematics. 676 $a164 700 $aHermes$b Hans$042101 702 $aHerman$b Gabor T. 702 $aPlassmann$b Ortwin 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827106603321 996 $aEnumerability, Decidability, Computability$9354898 997 $aUNINA