Classical Descriptive Set Theory

Передня обкладинка
Springer Science & Business Media, 6 груд. 2012 р. - 404 стор.
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory.
This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.
 

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Зміст

Perfect Polish Spaces
31
CHAPTER II
65
Standard Borel Spaces
73
Borel Sets as Clopen Sets
82
Borel Injections and Isomorphisms
89
Borel Sets and Measures
103
Uniformization Theorems
120
Partition Theorems
129
Separation Theorems
217
Regularity Properties
226
Capacities
234
CHAPTER IV
242
CoAnalytic Ranks
267
Rank Theory
281
Scales and Uniformization
299
CHAPTER V
313

Borel Determinacy
137
Games People Play
149
The Borel Hierarchy
167
Some Examples
179
The Baire Hierarchy
190
CHAPTER III
196
Universal and Complete Sets
205
Projective Determinacy
322
Epilogue
346
On Logical Notation
353
References
369
Symbols and Abbreviations
381
Index
387
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