The Gamified Katětov order embeds P(ω)/Fin, yielding antichains of size continuum and new non-modest degrees in the extended Weihrauch hierarchy.
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A computable variant of the gamified Katětov order on filters is isomorphic to the Lawvere-Tierney order, linking combinatorial complexity measures to computability in topos theory.
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The Gamified Kat\v{e}tov order is not linear (in fact, very much not so)
The Gamified Katětov order embeds P(ω)/Fin, yielding antichains of size continuum and new non-modest degrees in the extended Weihrauch hierarchy.
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What can Topology tell us about Logical Complexity?
A computable variant of the gamified Katětov order on filters is isomorphic to the Lawvere-Tierney order, linking combinatorial complexity measures to computability in topos theory.