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| Artikel-Nr.: 858A-9783540600596 Herst.-Nr.: 9783540600596 EAN/GTIN: 9783540600596 |
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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. Weitere Informationen: | | Author: | Arnold Miller | Verlag: | Springer Berlin | Sprache: | eng |
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| Weitere Suchbegriffe: Mathematica; Algebra; Function; logic; mathematical logic; proof; theorem; well-ordering principle, Mathematica, algebra, forcing, function, logic, mathematical logic, proof, set theory, theorem, well-ordering principle |
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