anupubba-nirodha
The 9 'successive extinctions', are the 8 extinctions reached through the 8 absorptions (jhāna, q.v.) and the extinction of feeling and perception' (s. nirodha-samāpatti), as it is said in A. IX, 31 and D. 33:
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"In him who has entered the 1st absorption, the sensuous perceptions (kāma-saññā) are extinguished.
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Having entered the 2nd absorption, thought-conception and discursive thinking (vitakkavicāra, q.v.) are extinguished.
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Having entered the 3rd absorption, rapture (pīti, q.v.) is extinguished.
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Having entered the 4th absorption, in-and-out breathing (assāsa-passāsa, q.v.) are extinguished.
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Having entered the sphere of boundless space (ākāsānañcāyatana), the corporeality perceptions (rūpa-saññā) are extinguished.
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Having entered the sphere of boundless consciousness (viññānañcāyatana), the perception of the sphere of boundless space is extinguished.
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Having entered the sphere of nothingness (ākiñcaññāyatana), the perception of the sphere of boundless consciousness is extinguished.
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Having entered the sphere of neither-perception-nor-non-perception (neva-saññā-nāsaññāyatana) the perception of the sphere of nothingness is extinguished.
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Having entered the extinction of perception and feeling (saññāvedayitanirodha) perception and feeling are extinguished."
For further details, s. jhāna, nirodha-samāpatti.