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Inhaltsangabe
Volume I: Part I. Games and Scales: Introduction to Part I 1. Notes on the theory of scales 2. Propagation of the scale property using games 3. Scales on $\sum_1^1$-sets 4. Inductive scales on inductive sets 5. The extent of scales in $\mathbf{L}(\mathbb{R})$ 6. The largest countable this, that, and the other 7. Scales in $\mathbf{L}(\mathbb{R})$ 8. Scales in $\mathbf{K}(\mathbb{R})$ 9. The real game quantifier propagates scales 10. Long games 11. The length-$\omega_1$ open game quantifier propagates scales Part II. Suslin Cardinals, Partition Properties, Homogeneity: Introduction to Part II 12. Suslin cardinals, $\kappa$-Suslin sets, and the scale property in the hyperprojective hierarchy 13. The axiom of determinacy, strong partition properties, and nonsingular measures 14. The equivalence of partition properties and determinacy 15. Generic codes for uncountable ordinals, partition properties, and elementary embeddings 16. A coding theorem for measures 17. The tree of a Moschovakis scale is homogeneous 18. Weakly homogeneous trees Bibliography Volume II: Part III. Wadge Degrees and Pointclasses: Introduction to Part III 19. Wadge degrees and descriptive set theory 20. A note on Wadge degrees 21. Some results in the Wadge hierarchy of Borel sets 22. The strength of Borel Wadge determinacy 23. Closure properties of pointclasses 24. The axiom of determinacy and the prewellordering property 25. Pointclasses and wellordered unions 26. More closure properties of pointclasses 27. More measures from AD 28. Early investigations of the degress of Borel sets Part IV. Projective Ordinals: Introduction to Part IV 29. Homogeneous trees and projective scales 30. AD and projective ordinals 31. A $\Delta_3^1$ coding of the subsets of $\omega_\omega$ 32. AD and projective ordinals 33. Projective sets and cardinal numbers: some questions related to the continuum problem 34. Regular cardinals without the weak partition property Bibliography Volume III: Part V. HOD and its Local Versions: Ordinal Definability in Models of Determinacy: Introduction to Part V 35. Partially playful universes 36. Ordinal games and playful models 37. Measurable cardinals in playful models 38. Introduction to Q-theory 39. On the theory of $\prod_3^1$ sets of reals, II 40. An inner models proof of the Kechris-Martin theorem 41. A theorem of Woodin on mouse sets 42. HOD as a core model Part VI. Recursion Theory: Recursion Theoretic Papers: Introduction to Part VI 43. On recursion in E and semi-Spector classes 44. On Spector classes 45. Trees and degrees 46. Definable functions on degrees 47. $\prod_2^1$ monotone inductive definitions 48. Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations Bibliography Volume IV: Part VII. Extensions of AD, Models with Choice: A Brief History of Determinacy 49. 'AD plus uniformization' is equivalent to 'half $AD_\mathbb{R}$' 50. The independence of DC from AD 51. Games of countable length 52. Some consistency results in ZFC using AD 53. Subsets of $\aleph_1$ constructible from a real 54. AD and the uniqueness of the supercompact measures on $\wp_{\omega_1}(\lambda)$ 55. The extender algebra and $\sum_1^2$-absoluteness Part VIII. Other Topics: 56. On Vaught's conjecture 57. Capacities and analytic sets 58. More saturated ideals 59. The fourteen Victoria Delfino problems and their status in the year 2020 Bibliography.
Volume I: Part I. Games and Scales: Introduction to Part I 1. Notes on the theory of scales 2. Propagation of the scale property using games 3. Scales on $\sum_1^1$-sets 4. Inductive scales on inductive sets 5. The extent of scales in $\mathbf{L}(\mathbb{R})$ 6. The largest countable this, that, and the other 7. Scales in $\mathbf{L}(\mathbb{R})$ 8. Scales in $\mathbf{K}(\mathbb{R})$ 9. The real game quantifier propagates scales 10. Long games 11. The length-$\omega_1$ open game quantifier propagates scales Part II. Suslin Cardinals, Partition Properties, Homogeneity: Introduction to Part II 12. Suslin cardinals, $\kappa$-Suslin sets, and the scale property in the hyperprojective hierarchy 13. The axiom of determinacy, strong partition properties, and nonsingular measures 14. The equivalence of partition properties and determinacy 15. Generic codes for uncountable ordinals, partition properties, and elementary embeddings 16. A coding theorem for measures 17. The tree of a Moschovakis scale is homogeneous 18. Weakly homogeneous trees Bibliography Volume II: Part III. Wadge Degrees and Pointclasses: Introduction to Part III 19. Wadge degrees and descriptive set theory 20. A note on Wadge degrees 21. Some results in the Wadge hierarchy of Borel sets 22. The strength of Borel Wadge determinacy 23. Closure properties of pointclasses 24. The axiom of determinacy and the prewellordering property 25. Pointclasses and wellordered unions 26. More closure properties of pointclasses 27. More measures from AD 28. Early investigations of the degress of Borel sets Part IV. Projective Ordinals: Introduction to Part IV 29. Homogeneous trees and projective scales 30. AD and projective ordinals 31. A $\Delta_3^1$ coding of the subsets of $\omega_\omega$ 32. AD and projective ordinals 33. Projective sets and cardinal numbers: some questions related to the continuum problem 34. Regular cardinals without the weak partition property Bibliography Volume III: Part V. HOD and its Local Versions: Ordinal Definability in Models of Determinacy: Introduction to Part V 35. Partially playful universes 36. Ordinal games and playful models 37. Measurable cardinals in playful models 38. Introduction to Q-theory 39. On the theory of $\prod_3^1$ sets of reals, II 40. An inner models proof of the Kechris-Martin theorem 41. A theorem of Woodin on mouse sets 42. HOD as a core model Part VI. Recursion Theory: Recursion Theoretic Papers: Introduction to Part VI 43. On recursion in E and semi-Spector classes 44. On Spector classes 45. Trees and degrees 46. Definable functions on degrees 47. $\prod_2^1$ monotone inductive definitions 48. Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations Bibliography Volume IV: Part VII. Extensions of AD, Models with Choice: A Brief History of Determinacy 49. 'AD plus uniformization' is equivalent to 'half $AD_\mathbb{R}$' 50. The independence of DC from AD 51. Games of countable length 52. Some consistency results in ZFC using AD 53. Subsets of $\aleph_1$ constructible from a real 54. AD and the uniqueness of the supercompact measures on $\wp_{\omega_1}(\lambda)$ 55. The extender algebra and $\sum_1^2$-absoluteness Part VIII. Other Topics: 56. On Vaught's conjecture 57. Capacities and analytic sets 58. More saturated ideals 59. The fourteen Victoria Delfino problems and their status in the year 2020 Bibliography.
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