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2008

Long Borel hierarchies

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Long Borel hierarchies
We show that there is a model of ZF in which the Borel hierarchy on the reals has length 2. This implies that 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 +1 levels for any given limit ordinal less than 2. We also show that assuming a large cardinal hypothesis there are models of ZF in which the Borel hierarchy is arbitrarily long. Contents
Arnold W. Miller
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where MLQ
Authors Arnold W. Miller
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