Buch, Englisch, Band 4, 133 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 224 g
Reihe: Lecture Notes in Logic
How to prove theorems about Borel sets the hard way
Buch, Englisch, Band 4, 133 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 224 g
Reihe: Lecture Notes in Logic
ISBN: 978-3-540-60059-6
Verlag: Springer Berlin Heidelberg
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
1 What are the reals, anyway?.- I On the length of Borel hierarchies.- 2 Borel Hierarchy.- 3 Abstract Borel hierarchies.- 4 Characteristic function of a sequence.- 5 Martin’s Axiom.- 6 Generic G?.- 7 ?-forcing.- 8 Boolean algebras.- 9 Borel order of a field of sets.- 10 CH and orders of separable metric spaces.- 11 Martin-Solovay Theorem.- 12 Boolean algebra of order ?1.- 13 Luzin sets.- 14 Cohen real model.- 15 The random real model.- 16 Covering number of an ideal.- II Analytic sets.- 17 Analytic sets.- 18 Constructible well-orderings.- 19 Hereditarily countable sets.- 20 Shoenfield Absoluteness.- 21 Mansfield-Solovay Theorem.- 22 Uniformity and Scales.- 23 Martin’s axiom and Constructibility.- 24
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$$ sets.- III Classical Separation Theorems.- 26 Souslin-Luzin Separation Theorem.- 27 Kleene Separation Theorem.- 28
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$$ equivalence relations.- 31 Borel metric spaces and lines in the plane.- 32
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