4
votes
2answers
262 views

Is the Turing equivalence relation the orbit equiv. relation of the action of a countable group?

The Turing equivalence relation on $\cal P(\mathbb{N})$ is defined by $A\equiv_T B$ iff $A\leq_T B$ and $B\leq_T A$. This is a countable Borel equivalence relation on the polish space $\cal ...
3
votes
1answer
313 views

Action on a compact group

If $G$ is an infinite compact group, how many orbits can $G$ have under the group action of its continuous automorphisms ?