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Let be an infinite iterated function system on [0,1] satisfying the open set condition with the open set (0,1) and let Λ be its attractor. Then to any x ∈ Λ (except at most countably many points) corresponds a unique sequence ${aₙ(x)}_{n≥1}$ of integers, called the digit sequence of x, such that $x = lim_{n→∞} f_{a₁(x)}∘ ⋯ ∘ f_{aₙ(x)}(1)$. We investigate the growth...
We show that Martin's conjecture on Π¹₁ functions uniformly $≤_T$-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 functions is equivalent over ZFC to $Σ¹_{2n+2}$-Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π¹₁ functions...
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