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

Miller, Arnold

Brossura

ISBN 10: 3540600590 ISBN 13: 9783540600596

Casa editrice: Springer, 1995

Riassunto

This advanced graduate course assumes some knowledge of forcing as well as some elementary mathematical logic, e.g. the Lowenheim-Skolem Theorem. The first half deals with the general area of Borel hierarchies, probing lines of enquiry such as the possible lengths of a Borel hierarchy in a separable metric space. The second half goes on to include Harrington's Theorem together with a proof and applications of Louveau's Theorem on hyperprojective parameters.

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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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 1995
• Lingua: Inglese
• ISBN 10: 3540600590
• ISBN 13: 9783540600596
• Rilegatura: Copertina flessibile
• Numero di pagine: 133
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania