4 problems

Completeness conjecture. This index set is $\Sigma^1_1$-complete.

Let $X$ be a compact Polish space with uncountably many points. An $A'$-computable presentation is a presentation of $X$ as a separable metric space computable relative to the Turi…

Separation conjecture. Most of these definitions should be separable from one another by direct relativisation of known effective results or by using Pontryagin duality and the cor…

Nonexistence conjecture. No contractible set has computable type.