03600nam 2200601 450 991048086640332120170822144302.01-4704-0480-X(CKB)3360000000465060(EBL)3114085(SSID)ssj0000888799(PQKBManifestationID)11566303(PQKBTitleCode)TC0000888799(PQKBWorkID)10865676(PQKB)11733427(MiAaPQ)EBC3114085(PPN)195417658(EXLCZ)99336000000046506020150417h20072007 uy 0engur|n|---|||||txtccrBorel liftings of Borel sets some decidable and undecidable statements /Gabriel Debs, Jean Saint RaymondProvidence, Rhode Island :American Mathematical Society,2007.©20071 online resource (134 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 187, Number 876"Volume 187, Number 876 (first of 4 numbers)."0-8218-3971-3 Includes bibliographical references and index.""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 """"Chapter 2. A Double-Tree Representation for Borel Sets """"2.1. Double-trees ""; ""2.2. Double-tree characterization of â??[sup(0)][sub(2)] sets""; ""2.3. Double-tree characterization of D(â??[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""""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""Memoirs of the American Mathematical Society ;Volume 187, Number 876.Borel setsDescriptive set theoryConstructibility (Set theory)Electronic books.Borel sets.Descriptive set theory.Constructibility (Set theory)511.322Debs Gabriel1952-909851Saint Raymond Jean1946-MiAaPQMiAaPQMiAaPQBOOK9910480866403321Borel liftings of Borel sets2035994UNINA