LEADER 03706nam 2200697 450 001 9910820376703321 005 20210512235919.0 010 $a3-11-038129-X 010 $a3-11-027564-3 024 7 $a10.1515/9783110275643 035 $a(CKB)3710000000461746 035 $a(EBL)1787099 035 $a(SSID)ssj0001531232 035 $a(PQKBManifestationID)12639607 035 $a(PQKBTitleCode)TC0001531232 035 $a(PQKBWorkID)11533200 035 $a(PQKB)10211360 035 $a(DE-B1597)174868 035 $a(OCoLC)919182882 035 $a(OCoLC)919338525 035 $a(DE-B1597)9783110275643 035 $a(Au-PeEL)EBL1787099 035 $a(CaPaEBR)ebr11087975 035 $a(CaONFJC)MIL821110 035 $a(CaSebORM)9783110381290 035 $a(MiAaPQ)EBC1787099 035 $a(EXLCZ)993710000000461746 100 $a20150820h20152015 uy 0 101 0 $aeng 135 $aurun#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aRecursion theory $ecomputational aspects of definability /$fChi Tat Chong, Liang Yu 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2015. 210 4$d©2015 215 $a1 online resource (322 p.) 225 1 $aDe Gruyter Series in Logic and Its Applications,$x1438-1893 ;$vVolume 8 300 $aDescription based upon print version of record. 311 $a3-11-027555-4 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$tPart I: Fundamental theory --$t1 An introduction to higher recursion theory --$t2 Hyperarithmetic theory --$t3 Admissibility and constructibility --$t4 The theory of ?1 1-sets --$t5 Recursion-theoretic forcing --$t6 Set theory --$tPart II: The story of Turing degrees --$t7 Classification of jump operators --$t8 The construction of ?1 1-sets --$t9 Independence results in recursion theory --$tPart III: Hyperarithmetic degrees and perfect set property --$t10 Rigidity and bi-interpretability of hyperdegrees --$t11 Basis theorems --$tPart IV: Higher randomness theory --$t12 Review of classical algorithmic randomness --$t13 More on hyperarithmetic theory --$t14 The theory of higher randomness --$tA Open problems --$tB An interview with Gerald E. Sacks --$tC Notations and symbols --$tBibliography --$tIndex --$tBackmatter 330 $aThis monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. 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