5 problems

Let $(W_i)_{i\in\mathbb{N}}$ be an effective enumeration of the computably enumerable sets, and write $W_i\approx W_j$ when the two sets lie in the same orbit under automorphisms o…

Let $A$ be a c.e. set. It has the outer splitting property if there are computable functions $f,h$ such that, for every $e$, $W_e=W_{f(e)}\sqcup W_{h(e)}$,…

Let $A$ be a c.e. set. Its complement $\overline{A}$ is semilow when the corresponding semilowness property holds, and $A$ is low when $A'\equiv_T\mathbf{0}'$. Two c.e. sets are au…

Let $A$ be a c.e. set whose orbit is properly $\Delta^0_{\alpha}$ for a finite $\alpha>8$, as in Theorem 3.2, and let $\mathcal{L}_{\omega_1,\omega}$ denote the infinitary logic use…

Let $A$ be a computably enumerable set and let $\boldsymbol{d}$ be a Turing degree. Write $A'$ for the Turing jump of $A$, and let $\mathcal{L}^*(A)$ denote the lattice structure a…