The axiom of Turing determinacy is a weakening of the full axiom of determinacy, $AD$, in which only games with payoff sets which are $\equiv\_T$-invariant are demanded to be determined.

In "Turing determinacy and the continuum hypothesis" (published in 1989), Ramez Sami writes:

> 
> "The main question so far unsettled in this particular domain can be roughly put this way: is it true that for any "reasonable" pointclass $\Gamma$ we have: Turing-Det$(\Gamma)\implies$Det$(\Gamma)$? In particular is it the case that: [over $ZF+DC$, presumably] Turing $AD$ implies $AD$?"
> 
> 
> * <http://link.springer.com/article/10.1007%2FBF01622874>, page 153
> 
> 
> 

My question is, what is the status of this question currently? Do we know whether Turing $AD$ is strictly weaker than $AD$? The only recent work I know of around Turing determinacy is from the reverse mathematical side ([http://www.math.cornell.edu/~shore/papers/pdf/TDet21.pdf](http://www.math.cornell.edu/%7Eshore/papers/pdf/TDet21.pdf)); I'm not at all familiar with the set theory on the subject.

(I vaguely recall that Turing determinacy implies that every Suslin set is determined, but I can't remember where I supposedly learned this "fact.")