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For questions about frames (=lattices with arbitrary joins and such that finite meets are distributive over those, such as the open sets of a topological set) and locales (the dual category to that of frames, seen as a generalization of topological spaces), as well as about pointfree (“pointless”) topology. This includes questions both of an algebraic nature about frames and of a topological nature about locales.

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What is the power of the “anti-halting” oracle?

The set $K_1 := \bigcap_{B\subseteq\mathbb{N}} (H_1(B) \Rrightarrow B)$ is inhabited, that is, the “anti-halting oracle” is trivial, i.e., can be simulated with a Turing machine (consequently, as expl …
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