Classical Descriptive Set Theory

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. Language: English