axiom of unique choice (whenever there is a function, there is a function)
axiom of decidable excluded middle (whenever something is true or false, it is true or false)
@typeswitch But consider: does the set of all sets which do not contain themselves contain itself?
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Russell's well behaving set (the set of all sets that contain themselves does contain itself)
@aquarial @wistahe@koyu.space the set of all sets that don't lead to terrible contradictions