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Has there ever been a proof technique to show that a language isn't in $\mathrm{P}$, by showing inductively there isn't any $k$ for which the language is in $\mathrm{TIME}(n^k)$?

e.g.: $L\notin \mathrm{TIME}(n^0)$,

$L\notin \mathrm{TIME}(n^k)\rightarrow L\notin \mathrm{TIME}(n^{k+1})$,

$\therefore L\notin \mathrm{P}$.

Is something of the sort feasible? Has it been used?

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Something like this is used in the definition of creative sets by Joseph and Young (1985). See the Wikipedia article on polynomial creativity. But their use is to concoct NP-hard sets with unusual properties (potential counterexamples to the Berman–Hartmanis conjecture rather than to say anything nontrivial about the complexity of any natural algorithmic problem.

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