| Invariant Descriptive Set Theory Contributor(s): Gao, Su (Author) |
|
 |
ISBN: 1584887931 ISBN-13: 9781584887935 Publisher: CRC Press OUR PRICE: $218.50 Product Type: Hardcover - Other Formats Published: September 2008 Annotation: Bringing together techniques from various areas of mathematics, this book presents an introduction to the basic concepts, methods, and results of invariant descriptive set theory. It reviews classical and effective descriptive set theory; studies Polish groups and their actions; and covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also describes infinitary logic, Scott analysis, and the isomorphism relation on natural classes of countable models. The book concludes with applications to classification problems and many benchmark equivalence relations. It also contains a large number of exercises at the end of most sections. |
| Additional Information |
| BISAC Categories: - Mathematics | Set Theory |
| Dewey: 511.322 |
| LCCN: 2008031545 |
| Series: Pure and Applied Mathematics |
| Physical Information: 1" H x 6.1" W x 9.3" (1.50 lbs) 392 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields. After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm-Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research. |