A universal Martin-Löf test exists

Decode the outputs of the $e$-th partial computable function as pairs $(k,\sigma )$, discarding malformed outputs. This enumerates a c.e. relation $W_e\subseteq \mathbb{N}\times \{0,1{\}}^{\ast }$, and every c.e. relation occurs for some $e$ because Universal and acceptable numberings enumerates all partial computable functions. Hence the relations $W_e$ enumerate every uniformly effectively open candidate sequence.

For candidate $e$, at component $k$ retain a newly enumerated cylinder only when the finite union retained so far would still have measure at most $2^{-k}$. The measure of a finite cylinder union is computable by reducing its strings to a finite prefix-free set. Thus the retained relation is uniformly c.e. and always obeys the component bound. If the candidate already is a Martin-Löf test, no cylinder is ever discarded, since every finite subunion has measure at most the final measure.

Let $V_n$ be the union of all retained $e$-components at level $n+e+1$. Dovetailing the enumerations makes $(V_n)$ uniformly effectively open, and subadditivity gives $\mu (V_n)\le {\sum }_e{2}^{-(n+e+1)}=2^{-n}\mathrm{.}$ It is therefore a test by Martin-Löf tests and random sequences. If $(U_k^e)$ is a genuine test, step 2.1 does not trim it, so $U_{n+e+1}^e\subseteq V_n$ for all $n$. Take $c_e=e+1$ to obtain the stated universality.