A dedekind finite borel set

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A dedekind finite borel set
In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if B ⊆ 2ω is a Gδσ-set then either B is countable or B contains a perfect subset. Second, we prove that if 2ω is the countable union of countable sets, then there exists an Fσδ set C ⊆ 2ω such that C is uncountable but contains no perfect subset. Finally, we construct a model of ZF in which we have an infinite Dedekind finite D ⊆ 2ω which is Fσδ. Contents
Arnold W. Miller
Added 12 May 2011
Updated 12 May 2011
Type Journal
Year 2011
Where AML
Authors Arnold W. Miller
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