We show that Martin’s conjecture on Π¹₁ functions uniformly ${\le }_T$-order preserving on a cone implies Π¹₁ Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant $\Pi {¹}_{2n+1}$ functions is equivalent over ZFC to $\Sigma {¹}_{2n+2}$-Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π¹₁ functions implies the consistency of the existence of a Woodin cardinal.