We study the question of the existence of non-mitotic sets in NP. We show under various hypotheses that:

• 1-tt-mitoticity and m-mitoticity differ on NP.
• 1-tt-reducibility and m-reducibility differ on NP.
• There exist non-T-autoreducible sets in NP (by a result from Ambos-Spies, these sets are neither T-mitotic nor m-mitotic).
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