Preface |
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ix | |
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Games and scales. Introduction to Part I |
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3 | (25) |
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Notes on the theory of scales |
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28 | (47) |
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Propagation of the scale property using games |
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75 | (15) |
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90 | (4) |
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Inductive scales on inductive sets |
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94 | (8) |
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Scales on coinductive sets |
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102 | (8) |
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The extent of scales in L(R) |
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110 | (11) |
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The largest countable this. that, and the other |
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121 | (9) |
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130 | (46) |
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176 | (33) |
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The real game quantifier propagates scales |
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209 | (14) |
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223 | (37) |
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The length-ω1 open game quantifier propagates scales |
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260 | (13) |
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PART II SUSLIN CARDINALS, PARTITION PROPERTIES, HOMOGENEITY |
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Suslin cardinals, partition properties, homogeneity. Introduction to Part II |
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273 | (41) |
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Suslin cardinals, κ-Suslin sets, and the scale property in the hyperprojective hierarchy |
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314 | (19) |
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The axiom of determinacy, strong partition properties, and nonsingular measures |
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333 | (22) |
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The equivalence of partition properties and determinacy |
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355 | (24) |
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Generic codes for uncountable ordinals, partition properties, and elementary embeddings |
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379 | (19) |
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A coding theorem for measures |
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398 | (6) |
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The tree of a Moschovakis scale is homogeneous |
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404 | (17) |
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421 | (18) |
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Bibliography |
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439 | (80) |
Preface |
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ix | |
Original Numbering |
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xiii | |
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PART III WADGE DEGREES AND POINTCLASSES |
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Wadge degrees and pointclasses. Introduction to Part III |
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3 | (21) |
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Wadge degrees and descriptive set theory |
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24 | (19) |
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43 | (4) |
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Some results in the Wadge hierarchy of Borel sets |
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47 | (27) |
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The strength of Borel Wadge determinacy |
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74 | (28) |
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Closure properties of pointclasses |
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102 | (16) |
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The axiom of determinacy and the prewellordering property |
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118 | (23) |
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Pointclasses and wellordered unions |
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141 | (13) |
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More closure properties of pointclasses |
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154 | (6) |
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160 | (6) |
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Early investigations of the degrees of Borel sets |
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166 | (33) |
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PART IV PROJECTIVE ORDINALS |
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Projective ordinals. Introduction to Part IV |
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199 | (71) |
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Homogeneous trees and projective scales |
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270 | (34) |
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AD and projective ordinals |
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304 | (42) |
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A Δ13 coding of the subsets of cam |
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346 | (18) |
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AD and the projective ordinals |
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364 | (120) |
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Projective sets and cardinal numbers: some questions related to the continuum problem |
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484 | (25) |
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Regular cardinals without the weak partition property |
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509 | (10) |
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Bibliography |
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519 | (2) |
Preface |
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vii | |
Original Numbering |
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xi | |
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PART V HOD AND ITS LOCAL VERSIONS |
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Ordinal definability in models of determinacy. Introduction to Part V |
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3 | (46) |
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Partially playful universes |
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49 | (37) |
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Ordinal games and playful models |
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86 | (29) |
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Measurable cardinals in playful models |
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115 | (11) |
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126 | (74) |
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On the theory of Π13 sets of reals, II |
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200 | (20) |
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An inner models proof of the Kechris-Martin theorem |
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220 | (23) |
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A theorem of Woodin on mouse sets |
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243 | (14) |
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257 | (92) |
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Recursion theoretic papers. Introduction to Part VI |
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349 | (6) |
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On recursion in E and semi-Spector classes |
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355 | (35) |
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390 | (34) |
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424 | (34) |
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Definable functions on degrees |
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458 | (18) |
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Π12 monotone inductive definitions |
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476 | (17) |
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Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations |
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493 | (28) |
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Bibliography |
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521 | |
Preface |
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vii | |
Original Numbering |
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xi | |
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PART VII EXTENSIONS OF AD, MODELS WITH CHOICE |
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A brief history of determinacy |
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3 | (58) |
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"AD plus Uniformization" is equivalent to "Half ADR" |
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61 | (5) |
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The independence of DC from AD |
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66 | (30) |
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Games of countable length |
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96 | (8) |
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Some consistency results in ZFC using AD |
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104 | (26) |
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Subsets of ℵ1 constructible from a real |
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130 | (6) |
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AD and the uniqueness of the supercompact measures on ω1 (λ) |
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136 | (5) |
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The extender algebra and Sf-absoluteness |
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141 | (38) |
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179 | (17) |
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Capacities and analytic sets |
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196 | (27) |
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223 | (25) |
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The fourteen Victoria Delfino problems and their status in the year 2020 |
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248 | (33) |
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Bibliography |
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281 | |