Eternal or everlasting is what is meant here.
To prove that it does necessarily apply, I will show you other scriptures to back this up...
2 Thessalonians 1:9
They will be punished with everlasting destruction and shut out from the presence of the Lord and from the majesty of his power
Jude 1:7
In a similar way, Sodom and Gomorrah and the surrounding towns gave themselves up to sexual immorality and perversion. They serve as an example of those who suffer the punishment of eternal fire.
Jude 1:13
They are wild waves of the sea, foaming up their shame; wandering stars, for whom blackest darkness has been reserved forever.
Revilation 14:9-11
A third angel followed them and said in a loud voice: “If anyone worships the beast and his image and receives his mark on the forehead or on the hand, he, too, will drink of the wine of God’s fury, which has been poured full strength into the cup of his wrath. He will be tormented with burning sulfur in the presence of the holy angels and of the Lamb. And the smoke of their torment rises for ever and ever. There is no rest day or night for those who worship the beast and his image, or for anyone who receives the mark of his name.”
I hope there is now no ambiguity as to whether it is eternal or not.
If you are able to read the Greek, you will find out that all of these verses rest on the same assumption as your earlier verses.
Gk.
aionion is the word in question. Does it refer to a time without end? Older translators typically thought so, and rendered the word accordingly: "everlasting." Modern translators, commentators and linguistics are more skeptical, and typically render the word as "eternal." The two English terms are actually quite different.
To demonstrate that
aionion does not ALWAYS mean "everlasting," here are two passages, one from John, one from Paul:
John 17:3 "This is
aionion life, that they may know You, the only true God, and Jesus Christ whom You have sent."
Rom. 16:25 "Now to Him who is able to establish you according to my gospel and the preaching of Jesus Christ, according to the revelation of the mystery which has been kept secret for
aionion ages..."
The verse from John uses
aionion to describe a kind of life that is qualitatively different from the life belonging to this age. John presents Jesus as the one who has come from heaven to bring the true knowledge of God to those who will believe. It has nothing to do with the future -- it is entirely concerned with present experience, an experience that is unlike any experience from our time or world.
The verse in Romans uses aionion to describe time prior to Jesus' earthly ministry. Unless you posit an endless time period stretching backwards, during which "the mystery" was kept secret, it is clear that
aionion isn't being used to denote time of unending duration. Rather, the time during which the mystery was kept secret was during an entirely different age, namely, before the breaking-in of God's kingdom, before the beginning of resurrection, before the divine presence with all the church through the Holy Spirit, etc.
In sum, no verse using the word
aionion can operate as a "proof-text" of the traditional doctrine of hell (the everlasting torment of the damned) without substantial contextual support. There are some texts in Matthew's gospel and Revelation that may qualify, given such exegetical work, but simply throwing verses around isn't going to go anywhere.
I know this is a sensitive issue and I hope that I have not offended or irritated you in any way.