LEADER 04776nam 2200637 450 001 9910788841703321 005 20170822144312.0 010 $a1-4704-0293-9 035 $a(CKB)3360000000464886 035 $a(EBL)3114509 035 $a(SSID)ssj0000910361 035 $a(PQKBManifestationID)11486552 035 $a(PQKBTitleCode)TC0000910361 035 $a(PQKBWorkID)10931835 035 $a(PQKB)11729855 035 $a(MiAaPQ)EBC3114509 035 $a(RPAM)12102310 035 $a(PPN)195415876 035 $a(EXLCZ)993360000000464886 100 $a20000711h20002000 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalytic quotients $etheory of liftings for quotients over analytic ideals on the integers /$fIlijas Farah 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2000] 210 4$dİ2000 215 $a1 online resource (201 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 702 300 $aDescription based upon print version of record. 311 $a0-8218-2117-2 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Preface""; ""Acknowledgments""; ""A note to the reader""; ""Introduction""; ""Chapter 1. Baire-measurable homomorphisms of analytic quotients""; ""1.1. Introduction""; ""1.2. Ideals induced by submeasures""; ""1.3. Preorderings on analytic quotients""; ""1.4. The Radona???Nikodym property""; ""1.5. Asymptotically additive liftings""; ""1.6. The Radona???Nikodym property of Fin and Fin x0""; ""1.7. A reformulation of Todorcevic's hypothesis""; ""1.8. Approximate homomorphisms and non-pathological submeasures""; ""1.9. The lifting theorem and the non-lifting theorem"" 327 $a""1.10. Permanence properties of quotients""""1.11. Simple FI?? P-ideals which are not summable""; ""1.12. The structure of summable ideals""; ""1.13. The structure of density ideals""; ""1.14. Remarks and questions""; ""Chapter 2. Open Coloring Axiom and uniformization""; ""2.1. Why Open Coloring Axiom?""; ""2.2. Coherent families of partial functions""; ""2.3. Coherent families of partitions""; ""2.4. a???[sub(2)]-reflection for coherent families""; ""2.5. Remarks and questions""; ""Chapter 3. Homomorphisms of analytic quotients under OCA""; ""3.1. Introduction"" 327 $a""3.2. Homomorphisms without Baire-measurable liftings""""3.3. Almost liftings and lifting theorems""; ""3.4. Applications: rigidity of analytic quotients""; ""3.5. Applications: quotients embeddable into analytic quotients""; ""3.6. Automorphism groups""; ""3.7. Homogeneity of analytic quotients""; ""3.8. Almost liftings of embeddings into P(N)/Fin""; ""3.9. Almost liftings of embeddings into P(N[sup(2)])/Fin x0""; ""3.10. Nonmeager hereditary sets""; ""3.11. Approximate homomorphisms; more on stabilizers""; ""3.12. A local version of the OCA lifting theorem"" 327 $a""3.13. The proof of the OCA lifting theorem for the analytic P-ideals""""3.14. Remarks and questions""; ""Chapter 4. Weak Extension Principle""; ""4.1. Introduction""; ""4.2. Dependence of functions on their variables""; ""4.3. Prime mappings""; ""4.4. Autohomeomorphisms of finite powers of I?²[sub(w)] and w*""; ""4.5. Cecha???Stone remainders of countable ordinals""; ""4.6. Some Parovicenko spaces under wEP""; ""4.7. Remainders of locally compact, countable spaces""; ""4.8. Almost liftings and duality""; ""4.9. OCA and MA imply wEP""; ""4.10. Versions of wEP""; ""4.11. Remarks and questions"" 327 $a""Chapter 5. Gaps and limits in analytic quotients""""5.1. Introduction""; ""5.2. Gaps in the quotient over Fin""; ""5.3. Gaps in the quotient over 0 x Fin""; ""5.4. Gaps in the quotient over Fin x0""; ""5.5. The Todorcevic separation property, TSP""; ""5.6. Tukey reductions of nonlinear gaps""; ""5.7. TSP in quotients over analytic P-ideals""; ""5.8. Quotients as reduced products""; ""5.9. Preservation of gaps""; ""5.10. An analytic Hausdorff gap""; ""5.11. Limits in analytic quotients""; ""5.12. A coherent family of functions""; ""5.13. Remarks and questions""; ""Bibliography""; ""Index"" 327 $a""A"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 702. 606 $aSet theory 606 $aAlgebra, Boolean 606 $aLifting theory 615 0$aSet theory. 615 0$aAlgebra, Boolean. 615 0$aLifting theory. 676 $a510 s 676 $a511.3/22 700 $aFarah$b Ilijas$f1966-$01566834 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788841703321 996 $aAnalytic quotients$93837747 997 $aUNINA