If 'feasible computation' is not co-extensional with polynomial time across all physically realizable models, the closure property of NP under polynomial reductions loses its unconditional force.

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Closure property(mathematics and logic): A quality of a set or category where if you perform a certain operation on things in that set, the result stays in that set—it doesn't break out of the group.
Co-extensional(describing when two things match up but aren't necessarily connected in a meaningful way): Having exactly the same members or applying to exactly the same things, even if for completely different reasons.
Feasible computation(This concept is being examined in the statement): A calculation or problem that a computer could actually solve in a reasonable amount of time, rather than taking forever.
NP (nondeterministic polynomial time)(Major complexity class based on nondeterministic model): The union over all natural numbers k of NTIME(n^k); the class of languages decidable by a nondeterministic Turing machine in polynomial time.

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