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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Descriptive Set Theory and Forcing: How to Prove Theorems about Borel Sets the Hard Way

Descriptive Set Theory and Forcing: How to Prove Theorems about Borel Sets the Hard Way

Miller, Arnold

Paperback

Series: Lecture Notes in Logic, Book 4

FictionGeneral Mathematics

ISBN10: 3540600590
ISBN13: 9783540600596
Publisher: Springer Nature
Published: Sep 18 1995
Pages: 133
Weight: 0.45
Height: 0.30 Width: 6.14 Depth: 9.21
Language: English
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.

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