LEADER 05586nam  2200697Ia 450 
001 9910813457003321
005 20240313221820.0
010   $a1-281-93434-8
010   $a9786611934347
010   $a981-279-405-0
035   $a(CKB)1000000000549533
035   $a(EBL)1193153
035   $a(SSID)ssj0000292343
035   $a(PQKBManifestationID)11237016
035   $a(PQKBTitleCode)TC0000292343
035   $a(PQKBWorkID)10269176
035   $a(PQKB)10355065
035   $a(MiAaPQ)EBC1193153
035   $a(WSP)00001767    
035   $a(Au-PeEL)EBL1193153
035   $a(CaPaEBR)ebr10698842
035   $a(CaONFJC)MIL193434
035   $a(OCoLC)820944486
035   $a(EXLCZ)991000000000549533
100   $a20080319d2008      uy         0
101 0 $aeng
135   $aurcn|||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aComputational prospects of infinity$hPart I$iTutorials /$feditors, Chitat Chong ... [et al.]
205   $a1st ed.
210   $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2008
215   $a1 online resource (264 p.)
225 1 $aLecture notes series / Institute for Mathematical Sciences, National University of Singapore ;$vv. 14
300   $aDescription based upon print version of record.
311   $a981-279-653-3 
320   $aIncludes bibliographical references.
327   $aCONTENTS; Foreword; Preface; Recursion Theory Tutorials; Five Lectures on Algorithmic Randomness Rod Downey; 1. Introduction; 2. Lecture 1: Kolmogorov complexity basics; 2.1. Plain complexity; 2.2. Symmetry of Information; 2.3. Pre.x-free complexity; 2.4. The Coding Theorem; 2.5. Pre.x-free symmetry of information; 2.6. Pre.x-free randomness; 2.7. The overgraph functions; 3. Lecture 2: Randomness for reals; 3.1. Martin-L ?of randomness; 3.2. Schnorr's Theorem and the computational paradigm; 3.3. Martingales and the prediction paradigm; 3.4. Super martingales and continuous semimeasures
327   $a3.5. Schnorr and computable randomness 4. Lecture 3: Randomness in general; 4.1. The de Leeuw, Moore, Shannon, Shapiro Theorem, and Sacks' Theorem; 4.2. Coding into randoms; 4.3. Kucera Coding; 4.4. n-randomness; 4.5. Notes on 2-randoms; 4.6. Kucera strikes again; 4.7. van Lambalgen's Theorem; 4.8. Effective 0-1 Laws; 4.9. Omega operators; 5. Lecture 4: Calibrating randomness; 5.1. Measures of relative randomness and the Kucera-Slaman Theorem; 5.2. The Density Theorem; 5.3. Other measures of relative randomness; 5.4. <C and <K.; 5.5. Outside of the randoms; 5.6.
327   $a5.7. Hausdor. Dimension 6. Lecture 5: Measure-theoretical injury arguments; 6.1. Risking measure; 6.2. 2-random degrees are hyperimmune; 6.3. Almost every degree is CEA; References; Global Properties of the Turing Degrees and the Turing Jump Theodore A. Slaman; 1. Introduction; 1.1. Style; 2. The coding lemma and the  rst order theory of the Turing degrees; 2.1. The coding lemma; 3. Properties of automorphisms of D; 3.1. Results of Nerode and Shore; 4. Slaman and Woodin analysis of Aut(D); 4.1. Persistent automorphisms; 4.2. Persistently extending persistent automorphisms
327   $a4.3. Persistence and reection 4.4. Generic persistence; 4.5. Denability of automorphisms of D; 4.6. Invariance of the double jump; 5. Denability in D; 5.1. Bi-interpretability; 6. The Turing jump; 6.1. Recursive enumerability; References; Set Theory Tutorials; Derived Models Associated to Mice John R. Steel; 1. Introduction; 2. Some background and preliminaries; 2.1. Homogeneously Suslin sets; 2.2. Hom1 iteration strategies; 2.3. The derived model; 2.4. Iterations to make RV = R; 2.5. Premice over a set; 3. Iteration independence for derived models of mice
327   $a4. Mouse operators and jump operators 5. The mouse set conjecture in D(M;   ); 6. The Solovay sequence in D(M;   ); 7. The  -transform; 8. A long Solovay sequence; 9. The mouse set conjectures: Framework of the induction; 10. The background universe N; 11. The L[E]-model Nx; 12. Two hybrid mouse operators at  0; 13. New mice modulo (y); 15. The consistency strength of AD+ +  0 <; 16. Global MSC implies the local MSC; 17. MSC implies capturing via R-mice; References; Tutorial Outline: Suitable Extender Sequences W. Hugh Woodin; 1. Introduction; 2. Generalized iteration trees
327   $a2.1. Long extenders
330   $aThis volume presents the written versions of the tutorial lectures given at the Workshop on Computational Prospects of Infinity, held from 18 June to 15 August 2005 at the Institute for Mathematical Sciences, National University of Singapore. It consists of articles by four of the leading experts in recursion theory (computability theory) and set theory. The survey paper of Rod Downey provides a comprehensive introduction to algorithmic randomness, one of the most active areas of current research in recursion theory. Theodore A Slaman's article is the first printed account of the ground-breaking
410  0$aLecture notes series (National University of Singapore. Institute for Mathematical Sciences) ;$vv. 14.
606   $aRecursion theory$vCongresses
606   $aSet theory$vCongresses
606   $aInfinite$vCongresses
615  0$aRecursion theory
615  0$aSet theory
615  0$aInfinite
676   $a511.322
701   $aChong$b C.-T$g(Chi-Tat),$f1949-$0441174
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910813457003321
996   $aComputational prospects of infinity$94012909
997   $aUNINA