And again he indicates so called "everlasting(aionios/eonian) punishment" (Mt.25:46) is temporary:
"That threats of aionios punishment are helpful for those immature who abstain from evil out of fear and not for love is repeated, e.g. in CC 6,26: "it is not helpful to go up to what will come beyond that punishment, for the sake of those who restrain themselves only with much difficulty, out of fear of the aionios punishment"; Hom. in Jer. 20 (19), 4: for a married woman it is better to believe that a faithless woman will undergo aionios punishment and keep faithful, rather than knowing the truth and becoming disloyal;" (p.178-9 in "The Christian Doctrine of Apokatastasis: A Critical Assessment from the New Testament to Eriugena" by Ilaria Ramelli, Brill, 2013, 890 p.)
Origen speaking of "after eternal life" and "beyond eternal life", is supported also by:
Evagrius's Kephalaia Gnostika
Evagrius's Kephalaia Gnostika: A New Translation of the Unreformed Text from the Syriac (Writings from the Greco-Roman World), By Ilaria L.E. Ramelli (see pages 10- 11 at the url above).
Where again Origen refers to what is after eternal life, as well as after "the ages", beyond "ages of the ages" [often mistranslated forever & ever] and all ages.
https://www.amazon.com/Evagriuss-Kephalaia-Gnostika-Translation-Greco-Roman/dp/1628370394
In the Greek Old Testament (LXX, Septuagint) of Isaiah 54:4 the word aionios appears and is used of finite duration:
4 You should not fear that you were disgraced, nor should you feel ashamed that you were berated. For shame everlasting(aionios) you shall forget; and the scorn of your widowhood in no way shall you remember any longer (Apostolic Bible Polygot, LXX)
The same phrase, and Greek words, for "shame everlasting"(aionios) in Isa.54:4 occur again at Dan.12:2 LXX, which i have higlighted within the brackets:
Dan.12:2 καὶ πολλοὶ τῶν καθευδόντων ἐν γῆς χώματι ἐξεγερθήσονται οὗτοι εἰς ζωὴν αἰώνιον καὶ οὗτοι εἰς ὀνειδισμὸν καὶ εἰς [αἰσχύνην αἰώνιον]
Isa.54:4 μὴ φοβοῦ ὅτι κατῃσχύνθης μηδὲ ἐντραπῇς ὅτι ὠνειδίσθης ὅτι [αἰσχύνην αἰώνιον] ἐπιλήσῃ καὶ ὄνειδος τῆς χηρείας σου οὐ μὴ μνησθήσῃ
Kata Biblon Wiki Lexicon - ??????? - shame/disgrace/dishonor (n.)
Strong's Greek: 152. ??????? (aischuné) -- shame
In Isa.54:4 aionios/eonian is finite: "For shame everlasting[eonian] you shall forget".
In that light we might consider that the exact same phrase from the LXX scholars, "shame everlasting [eonian]" in Dan.12:2, may also be finite.
Consider also whether aionios is finite in these Greek Old Testament passages:
I have considered the days of old, the years of ancient(aionios) times. (Psa.77:5)
Don’t move the ancient(aionios) boundary stone, which your fathers have set up. (Prov.22:28)
Don’t move the ancient(aionios) boundary stone. Don’t encroach on the fields of the fatherless: (Prov.23:10)
Those from among you will rebuild the ancient(aionios) ruins; You will raise up the age-old(aionios) foundations;... (Isa 58:12a)
Thus says the Lord Yahweh: Because the enemy has said against you, Aha! and, The ancient(aionios) high places are ours in possession; (Ezek.36:2)
Because of thy having an enmity age-during(aionios)... (Ezek.35:5a)
They will rebuild the perpetual(aionios) ruins and restore the places that were desolate; (Isa.61:4a)
I went down to the bottoms of the mountains. The earth barred me in forever(aionios): yet have you brought up my life from the pit, Yahweh my God. (Jonah 2:6)
He beat back His foes; He gave them lasting(aionios) shame. (Psa.78:66)
Will you keep the old(aionios) way, which wicked men have trodden (Job 22:15)
Will it make an agreement with you for you to take it as your slave for life(aionios)? (Job 41:4)
’Will you not fear me?" says The Lord "will you not be cautious in front of my face? The One who appointed the sand to be the boundary to the sea, by perpetual(aionios) decree, that it will not cross over though it will be agitated it is not able and though the waves resound within her yet she will not overstep it. (Jer.5:22)
Their land will be an object of horror and of lasting(aionios) scorn; all who pass by will be appalled and will shake their heads. (Jer.18:16)
Behold I will send, and take all the kindreds of the north, saith the Lord, and Nabuchodonosor the king of Babylon my servant: and I will bring them against this land, and against the inhabitants thereof, and against all the nations that are round about it: and I will destroy them, and make them an astonishment and a hissing, and perpetual(aionios) desolations. (Jer.25:9)
And it shall come to pass, when seventy years are accomplished, that I will punish the king of Babylon, and that nation, saith the LORD, for their iniquity, and the land of the Chaldeans; and I will make it perpetual(aionios) desolations. (Jer.25:12)
In their heat I will make their feasts, and I will make them drunken, that they may rejoice, and sleep a perpetual(aionios) sleep, and not wake, saith the LORD. (Jer.51:39)
When I shall bring thee down with them that descend into the pit, with the people of old time, and shall set thee in the low parts of the earth, in places desolate of old(aionios),with them that go down to the pit, that thou be not inhabited; and I shall set glory in the land of the living; (Ezek.26:20)
I will make you a perpetual(aionios) desolation, and your cities shall not be inhabited; and you shall know that I am Yahweh. (Ezek.35:9)
From those sleeping in the soil of the ground many shall awake, these to eonian(aionios) life and these to reproach for eonian(aionios) repulsion. (Daniel 12:2)
Thus says Yahweh, “Stand in the ways and see, and ask for the old(aionios) paths, ‘Where is the good way?’ and walk in it, and you will find rest for your souls. But they said, ‘We will not walk in it.’ (Jer.6:16)
For my people have forgotten me, they have burned incense to false gods; and they have been made to stumble in their ways, in the ancient(aionios) paths, to walk in byways,in a way not built up; (Jer.18:15)
Then he remembered the days of old(aionios), Moses and his people, saying, Where is he who brought them up out of the sea with the shepherds of his flock?where is he who put his holy Spirit in the midst of them? (Isa.63:11)
Greek scholar Marvin Vincent said:
"The adjective aionios, in like manner, carries the idea of “time.” Neither the noun nor the adjective, in themselves, carry the sense of endless or everlasting, though they may acquire that sense by their connotation. Aionios means “enduring through or pertaining to a period of time.” Both the noun and the adjective are applied to limited periods."
"The same is true of aionios in the Septuagint. Out of 150 instances in the Septuagint, four-fifths imply limited duration".
"..."The word always carries the notion of time, and not of eternity. It always means a period of time. Otherwise it would be impossible to account for the plural, or for such qualifying expressions as this age, or the age to come. It does not mean something endless or everlasting."
"...The adjective aionios in like manner carries the idea of time. Neither the noun nor the adjective, in themselves, carry the sense of endless or everlasting."
".... Aionios means enduring through or pertaining to a period of time. Both the noun and the adjective are applied to limited periods."
"...Words which are habitually applied to things temporal or material can not carry in themselves the sense of endlessness."
"...There is a word for everlasting if that idea is demanded."
https://www.hopefaithprayer.com/books/Word-Studies-in-the-New-Testament-Vol-3&4-Marvin-R-Vincent.pdf
Word Studies in the New Testament
Eastern Orthodox scholar David Bentley Hart comments in his extensive notes (Concluding Scientific Postscript) re aionios following his translation of the New Testament:
"...John Chrysostom, in his commentary on Ephesians, even used the word aionios of the kingdom of the devil specifically to indicate that it is temporary (for it will last only until the end of the present age, he explains). In the early centuries of the church, especially in the Greek and Syrian East, the lexical plasticity of the noun and the adjective was fully appreciated -and often exploited - by a number of Christian theologians and exegetes (especially such explicit universalists as the great Alexandrians Clement and Origen, the "pillar of orthodoxy" Gregory of Nyssa and his equally redoubtable sister Makrina, the great Syrian fathers Diodore of Tarsus, Theodore of Mopsuestia, Theodoret of Cyrus, and Isaac of Ninevah, and so on, as well as many other more rhetorically reserved universalists, such as Gregory of Nazianzus)."
"Late in the fourth century, for instance, Basil the Great, bishop of Caesarea, reported that the vast majority of his fellow Christians (at least, in the Greek-speaking East with which he was familiar) assumed that "hell" is not an eternal condition, and that the "aionios punishment" of the age to come would end when the soul had been purified of its sins and thus prepared for union with God. Well into the sixth century, the great Platonist philosopher Olympiodorus the Younger could state as rather obvious that the suffering of wicked souls in Tartarus is certainly not endless, atelevtos, but is merely aionios; and the squalidly brutal and witless Christian emperor Justinian, as part of his campaign to extinguish the universalism of the "Origenists", found it necessary to substitute the word atelevtetos for aionios when describing the punishments of hell, since the latter word was not decisive..."
"As late as the thirteenth century, the East Syrian bishop Solomon of Bostra, in his authoritative compilation of the teachings of the "holy fathers" of Syrian Christian tradition, simply stated as a matter of fact that in the New Testament le-alam (the Syriac rendering of aionios) does not mean eternal, and that of course hell is not endless. And the fourteenth-century East Syrian Patriarch Timotheus II thought it uncontroversial to assert that the aionios pains of hell will come to an end when the souls cleansed by them, through the prayers of the saints, enter paradise" (The New Testament: A Translation, by David Bentley Hart, 2017, p.539-540).
https://www.amazon.com/New-Testament-David-Bentley-Hart/dp/0300186096