| Descriptive Set Theory and Forcing: How to Prove Theorems about Borel Sets the Hard Way 1995 Edition Contributor(s): Miller, Arnold (Author) |
|
 |
ISBN: 3540600590 ISBN-13: 9783540600596 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: September 1995 |
| Additional Information |
| BISAC Categories: - Mathematics | Set Theory - Mathematics | Logic |
| Dewey: 511.322 |
| LCCN: 95032951 |
| Series: Lecture Notes in Logic |
| Physical Information: 0.3" H x 6.14" W x 9.21" (0.45 lbs) 133 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: An advanced graduate course. Some knowledge of forcing is assumed, and some elementary Mathematical Logic, e.g. the Lowenheim-Skolem Theorem. A student with one semester of mathematical logic and 1 of set theory should be prepared to read these notes. The first half deals with the general area of Borel hierarchies. What are the possible lengths of a Borel hierarchy in a separable metric space? Lebesgue showed that in an uncountable complete separable metric space the Borel hierarchy has uncountably many distinct levels, but for incomplete spaces the answer is independent. The second half includes Harrington's Theorem - it is consistent to have sets on the second level of the projective hierarchy of arbitrary size less than the continuum and a proof and appl- ications of Louveau's Theorem on hyperprojective parameters. |