If P vs NP remains open, the semantic content of 'proper subset' in complexity theory may be underdetermined in ways that weaken extensional confidence in related hierarchy claims.

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Complexity theory(where analogous issues might appear): A branch of computer science and mathematics that studies how difficult different problems are to solve and how much computational power they require.
Hierarchy claims(as used in complexity theory and logic): Statements that different categories, levels, or types of things can be ranked or ordered from simpler to more complex.
P vs NP(the general computational problem being restricted by the theorem): One of the most important unsolved problems in computer science asking whether two different classes of problems (those easy to solve and those easy to check) are actually the same.
Proper subset(mathematical/computational): A collection that contains some, but not all, of the items in another collection. For example, all dogs are a proper subset of all animals, since there are animals that aren't dogs.

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