Instance reducibility and Weihrauch degrees

We identify a notion of reducibility between predicates, called instance reducibility, which commonly appears in reverse constructive mathematics. The can be generally used to compare and classify various principles studied mathematics (formal Church's thesis, Brouwer's Continuity principle Fan theorem, Excluded middle, Limited principle, Function choice, Markov's etc.). show that the degrees form frame, i.e., complete lattice finite infima distribute over set-indexed suprema. They turn out equivalent frame upper sets truth values, ordered by Smyth partial order. study overall structure lattice: subobject classifier embeds into two different ways, one monotone other antimonotone, $\lnot\lnot$-dense coincide with those are reducible degree middle. give an explicit formulation relative realizability topos, call these extended Weihrauch degrees, because Kleene-Vesley modest correspond precisely degrees. improve equipping them computable suprema, implication, ability control access parameters computation results, widening scope reducibility.