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Jan 4 at 21:40 comment added Andrej Bauer A similar observation is this: in $\mathcal{K}_1$ the relation "$n \bullet m$ is defined" is semidecidable, but in $\mathcal{K}_2$ the relation "$\alpha \bullet \beta$ is defined" is a $\Pi^0_2$ statement (for every output cell there are initial segments of $\alpha$ and $\beta$ that determine its value).
Jan 4 at 20:57 history answered Gro-Tsen CC BY-SA 4.0