LEADER 03625nam 2200613 450 001 9910829174403321 005 20170822144302.0 010 $a1-4704-0480-X 035 $a(CKB)3360000000465060 035 $a(EBL)3114085 035 $a(SSID)ssj0000888799 035 $a(PQKBManifestationID)11566303 035 $a(PQKBTitleCode)TC0000888799 035 $a(PQKBWorkID)10865676 035 $a(PQKB)11733427 035 $a(MiAaPQ)EBC3114085 035 $a(RPAM)14685372 035 $a(PPN)195417658 035 $a(EXLCZ)993360000000465060 100 $a20150417h20072007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBorel liftings of Borel sets $esome decidable and undecidable statements /$fGabriel Debs, Jean Saint Raymond 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2007. 210 4$dİ2007 215 $a1 online resource (134 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 187, Number 876 300 $a"Volume 187, Number 876 (first of 4 numbers)." 311 $a0-8218-3971-3 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Introduction ""; ""0.1. Descriptive classes: ""; ""0.2. An elementary topological problem: ""; ""0.3. Continuous and Borel liftings: ""; ""0.4. Main result ""; ""0.5. Application 1 ""; ""0.6. Application 2 ""; ""0.7. Application 3 ""; ""Chapter 1. A Tree Representation for Borel Sets ""; ""1.1. Trees ""; ""1.2. Distinguished subrelation ""; ""1.3. Canonical mapping of a distinguished subtree ""; ""1.4. Uniformly distinguished subtree ""; ""1.5. Tree products ""; ""1.6. Tree expansions and representations of Borel sets ""; ""1.7. Regular expansions and representations "" 327 $a""Chapter 2. A Double-Tree Representation for Borel Sets """"2.1. Double-trees ""; ""2.2. Double-tree characterization of a???[sup(0)][sub(2)] sets""; ""2.3. Double-tree characterization of D(a???[sup(0)][sub(2)]) sets""; ""2.4. Appendix : extension to Wadge classes""; ""Chapter 3. Two Applications of the Tree Representation""; ""3.1. Resolution of quasi-strategies""; ""3.2. Hurewicz type results""; ""3.3. A Borel separation result""; ""Chapter 4. Borel Liftings of Borel Sets""; ""4.1. Borel liftings of bounded rank""; ""4.2. Borel liftings of unbounded rank"" 327 $a""4.3. Solution to Ostrovsky's problem""""4.4. Borel liftings in coanalytic sets""; ""Chapter 5. More Consequences and Reverse Results""; ""5.1. Some boudedness principles""; ""5.2. Reverse results""; ""5.3. Conclusion""; ""5.4. Appendix: A Perfect Set Theorem for a Class of Equivalence Relations""; ""Chapter 6. Proof of The Main Result""; ""6.1. Sketch of the proof""; ""6.2. Labeling games with delay""; ""6.3. Proof of the basic case""; ""6.4. Proof of the general limit case""; ""6.5. Proof of the general successor case""; ""Bibliography""; ""Index"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 187, Number 876. 606 $aBorel sets 606 $aDescriptive set theory 606 $aConstructibility (Set theory) 615 0$aBorel sets. 615 0$aDescriptive set theory. 615 0$aConstructibility (Set theory) 676 $a511.322 686 $a31.10$2bcl 700 $aDebs$b Gabriel$f1952-$01650803 702 $aSaint Raymond$b Jean$f1946- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910829174403321 996 $aBorel liftings of Borel sets$94000382 997 $aUNINA