In (2), by "variables" I meant parameters, such as dimension.

I mean you have to define $\emptyset$ to be the smallest, or the largest, and it doesn't matter which you choose as long as you stick to your decision.

@Greg Kuperberg: well, as long as you have a co-meager set of measure 0, such as in the classical example from Oxtoby's book, then you have that. What's neat about Andreas Blass' example, though, is that it is very intuitive that it should have measure 0 and be comeager.

In more detail: if $a\le_T b$ then $a=\Phi^b$ for some Turing functional $\Phi$. The set $\Phi^b$ is $\Sigma_1(b)$ definable (actually $\Delta_1(b)$ definable here since $\Phi^b$ is total).