Higher Randomness and Forcing with Closed Sets - Archive ouverte HAL
Journal Articles Theory of Computing Systems Year : 2016

Higher Randomness and Forcing with Closed Sets

Abstract

Kechris showed in [9] that there exists a largest Π11 set of measure 0. Due to its universal nature, it was conjectured by many that this nullset has a high Borel rank. In this paper, we refute this conjecture and show that this nullset is merely Σ03. Together with a result of Liang Yu, our result also implies that the exact Borel complexity of this set is Σ03. To do this proof, we develop the machinery of effective randomness and effective Solovay genericity, investigating the connections between those notions and effective domination properties.
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Dates and versions

hal-01397294 , version 1 (15-11-2016)

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Cite

Benoit Monin. Higher Randomness and Forcing with Closed Sets. Theory of Computing Systems, 2016, ⟨10.1007/s00224-016-9681-5⟩. ⟨hal-01397294⟩

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