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The Davis-Putnam-Robinson-Matiyasevich theorem is:
Diophantine is equivalent to listable
This result has some known applications:
(1) Prime-producing polynomials.
(2) Diophantine statement of the Riemann hypothesis.
The abc conjecture asserts that whenever $a,b,c$ are pairwise coprime positi...
Consider a stochastic approximation process with
$$x_{t+1} = x_t + \frac{1}{t} (g(x_t)+u_t)$$
where $(u_s)_s$ is a sequence of i.i.d. shocks.
Assume $g$ is Lipschitz, $u_t$ has finite variance, and that
$(x_s)_s$ is bounded with probability one.
Furthermore, assume that
$$
C = \{ x \in \mathbb...
