# computability – Is there a \$Sigma^0_3\$ variant of the halting problem?

In terms of the arithmetical hierarchy, the halting problem is known to be $$Sigma^0_1$$-complete, and the so-called universal halting problem, is the problem of determining whether a given computer program will halt for every input, is known to be $$Pi^0_2$$-complete.

Is there a natural $$Sigma^0_3$$-complete variant of the halting problem?