Buch, Englisch, 404 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1710 g
Buch, Englisch, 404 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1710 g
Reihe: Graduate Texts in Mathematics
ISBN: 978-0-387-94374-9
Verlag: Springer
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
I Polish Spaces.- 1. Topological and Metric Spaces.- 2. Trees.- 3. Polish Spaces.- 4. Compact Metrizable Spaces.- 5. Locally Compact Spaces.- 6. Perfect Polish Spaces.- 7.Zero-dimensional Spaces.- 8. Baire Category.- 9. Polish Groups.- II Borel Sets.- 10. Measurable Spaces and Functions.- 11. Borel Sets and Functions.- 12. Standard Borel Spaces.- 13. Borel Sets as Clopen Sets.- 14. Analytic Sets and the Separation Theorem.- 15. Borel Injections and Isomorphisms.- 16. Borel Sets and Baire Category.- 17. Borel Sets and Measures.- 18. Uniformization Theorems.- 19. Partition Theorems.- 20. Borel Determinacy.- 21. Games People Play.- 22. The Borel Hierarchy.- 23. Some Examples.- 24. The Baire Hierarchy.- III Analytic Sets.- 25. Representations of Analytic Sets.- 26. Universal and Complete Sets.- 27. Examples.- 28. Separation Theorems.- 29. Regularity Properties.- 30. Capacities.- 31. Analytic Well-founded Relations.- IV Co-Analytic Sets.- 32. Review.- 33. Examples.- 34. Co-Analytic Ranks.- 35. Rank Theory.- 36. Scales and Uniformiiatiou.- V Projective Sets.- 37. The Projective Hierarchy.- 38. Projective Determinacy.- 39. The Periodicity Theorems.- 40. Epilogue.- Appendix A. Ordinals and Cardinals.- Appendix B. Well-founded Relations.- Appendix C. On Logical Notation.- Notes and Hints.- References.- Symbols and Abbreviations.
