Published online by Cambridge University Press: 12 March 2014
We show that Sacks' and Shoenfield's analogs of jump inversion fail for both tt- and wtt-reducibilities in a strong way. In particular we show that there is a δ20 set B >tt ∅′ such that there is no c.e. set A with A′ ≡wttB. We also show that there is a Σ20 set C >tt ∅′ such that there is no δ20 set D with D′ ≡wttC.