β
Phillifent, John T.
π
Fiction
π
2018
π
Analog
π
English
β 191 KB
π 2 views
β¦ LIBER β¦
Long Borel hierarchies
β Scribed by Arnold W. Miller
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 211 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We show that there is a model of ZF in which the Borel hierarchy on the reals has length Ο~2~. This implies that Ο~1~ has countable cofinality, so the axiom of choice fails very badly in our model. A similar argument produces models of ZF in which the Borel hierarchy has exactly Ξ» + 1 levels for any given limit ordinal Ξ» less than Ο~2~. We also show that assuming a large cardinal hypothesis there are models of ZF in which the Borel hierarchy is arbitrarily long. (Β© 2008 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
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β
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π
Fiction
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