Abstract

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 ${\mathrm{\Delta }}_{2}^{0}$ set B > tt ∅′ such that there is no c.e. set A with A′ ≡ wtt B. We also show that there is a ${\mathrm{\Sigma }}_{2}^{0}$ set C > tt ∅′ such that there is no ${\mathrm{\Delta }}_{2}^{0}$ set D with D′ ≡ wtt C