3 problems

Incomparability conjecture. There are block functions $f$ and $g$ on $(\omega,<)$ whose degree spectra on a cone are incomparable: neither degree spectrum contains the other.

Degree-spectrum conjecture. If the degree spectrum of $f$ on $(\omega,<)$ is equal to all c.e. degrees, then the successor is recoverable from $f$ on $(\omega,<)$.

A Turing degree is low$_n$ if its $n$th Turing jump has the same degree as the $n$th jump of the computable degree. Consider spectra of structures, namely the sets of Turing degree…