LEADER 04159nam 22006855 450 001 9911047799303321 005 20251119175338.0 010 $a9783031924330$b(ebook) 024 7 $a10.1007/978-3-031-92433-0 035 $a(CKB)40402032800041 035 $a(MiAaPQ)EBC32269956 035 $a(Au-PeEL)EBL32269956 035 $a(DE-He213)978-3-031-92433-0 035 $a(OCoLC)1535242436 035 $a(EXLCZ)9940402032800041 100 $a20250821h20262026 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComputable structure theory $ea unified approach /$fRodney G. Downey, Alexander Melnikov 205 $a1st ed. 210 1$aCham :$cSpringer,$d[2026] 210 4$dİ2026 215 $a1 online resource (xii, 540 pages) $cillustrations 225 1 $aTheory and applications of computability, In cooperation with the Association Computability in Europe,$x2190-6203 311 08$a9783031924323 320 $aIncludes bibliographical references and index. 327 $aPart I Foundation of Computability -- 1. Introduction -- 2. Basics of Computability Theory -- 3. Computable Algebraic Structures -- 4. Computable Separable Spaces -- Part II Computable Duality -- 5. Computable Boolean Algebras -- 6. Computable Stone Spaces -- 7. Computable Abelian Groups -- 8. Computable Connected Compact Spaces -- Part III Computability and Classification Problems. 9. The Analytical Hierarchy and ?11-completeness -- 10. Computable Categoricity -- 11. Computable Banach Spaces with Applications -- 12. Resource Bounded Computation -- Part IV Non-computability and Randomness. 13. Randomness -- 14. Degree Spectra -- 15 -- Computable Transfinite Analysis. 330 $aThis is the first book which gives a unified theory for countable and uncountable computable structures. The work treats computable linear orderings, graphs, groups and Boolean algebras unified with computable metric and Banach spaces, profinite groups, and the like. Further, it provides the first account of these that exploits effective versions of dualities, such as Stone and Pontryagin dualities. The themes are effective classification and enumeration. Topics and features: · Delivers a self-contained, gentle introduction to priority arguments, directly applying them in algebraic contexts · Includes extensive exercises that both cement and amplify the materials · Provides complete introduction to the basics of computable analysis, particularly in the context of computable structures · Offers the first monograph treatment of computable Polish groups, effective profinite groups via Stone duality, and effective abelian groups via Pontryagin duality · Presents the first book treatment of Friedberg enumerations of structures This unique volume is aimed at graduate students and researchers in computability theory, as well as mathematicians seeking to understand the algorithmic content of structure theory. Being self-contained, it provides ample opportunity for self-study. 410 0$aTheory and applications of computability.$x2190-6203 606 $aComputer science 606 $aComputer arithmetic and logic units 606 $aAlgorithms 606 $aComputable functions 606 $aRecursion theory 606 $aTheory of Computation 606 $aArithmetic and Logic Structures 606 $aAlgorithms 606 $aComputability and Recursion Theory 615 0$aComputer science. 615 0$aComputer arithmetic and logic units. 615 0$aAlgorithms. 615 0$aComputable functions. 615 0$aRecursion theory. 615 14$aTheory of Computation. 615 24$aArithmetic and Logic Structures. 615 24$aAlgorithms. 615 24$aComputability and Recursion Theory. 676 $a511.352 700 $aDowney$b R. G. ?q (Rod G.)$01864387 701 $aMelnikov$b Alexander$0150247 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911047799303321 996 $aComputable structure theory$94471202 997 $aUNINA