Descriptive Set Theory and Forcing: How to prove theorems about Borel sets the hard way (Lecture Notes in Logic, 4) - Softcover

Miller, Arnold

Softcover

ISBN 10: 3540600590 ISBN 13: 9783540600596

Publisher: Springer, 1995

Synopsis

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.

About this title

Book Description

These notes develop the theory of descriptive sets, leading up to a new proof of Louveau's separation theorem for analytic sets. A first course in mathematical logic and set theory is assumed, making this book suitable for advanced students and researchers.

About the Author

Arnold W. Miller works in the Department of Mathematics at the University of Wisconsin, Madison.

Edition details

• Publisher: Springer
• Publication date: 1995
• Language: English
• ISBN 10: 3540600590
• ISBN 13: 9783540600596
• Binding: Paperback
• Number of pages: 137