Gospel Guidebook: Getting and Keeping It Right 
Aionios: "In Eternity" with "Everlasting Consequences"
Background
In my articles God is the Savior of All Men and Revelation 14:9-11 and Christian Universalism, I suggested that the expressions "eternal punishment" in Matthew 25:46 and "the smoke of their torment ascendeth up for ever and ever" in Revelation 14:11 refer to "temporal punishment in eternity that has everlasting consequences." In this article, I would like to pursue this suggestion further. However, as prerequisite material, I recommend that readers read those two articles first.
In Eternity
It seems to me that when most people see the word "eternal" in the Bible, they immediately interpret it as if it were an adverb instead of an adjective. For example, "eternal punishment" is often interpreted as "eternally punishing." Now, while I don't doubt that "eternal" has quantitative properties, I also don't think its qualitative properties should be ignored. When viewed qualitatively, "eternal" is descriptive of what happens "in eternity." To support this view, I would like to look at a few scriptures. Since I need a literal translation for this, I will be using the Revised American Standard Version Textus Receptus Edition.
Luke 18:30
In Luke 18:29-30, we read the following: 29 And he said unto them, Verily I say unto you, There is no man that hath left house, or parents, or brethren, or wife, or children, for the kingdom of God's sake, 30 who shall not receive manifold more in this time, and in the age to come, eternal life. In this verse, we see that "receiving manifold more in this time, and in the age to come" describes, at least to some extent, "eternal life." It is commonly accepted that "the age to come" refers to "eternity" because it is "the Age of Messiah," which has no end (cf. Luke 1:33, Daniel 7:14). Therefore, we see that at least one aspect of receiving "eternal life" refers to receiving "manifold more in eternity."
Mark 3:28-29 & Matthew 12:31-32
In Mark 3:28-29, we read the following: 28 Verily I say unto you, All sins shall be forgiven unto the sons of men, and blasphemies wherewith soever they shall blaspheme: 29 but whosoever shall blaspheme against the Holy Spirit hath not forgiveness for ever, but is subject to eternal judgment: In a parallel passage in Matthew 12:31-32, we read, 31 Therefore I say unto you, Every sin and blasphemy shall be forgiven unto men; but the blasphemy against the Spirit shall not be forgiven unto men. 32 And whosoever shall speak a word against the Son of man, it shall be forgiven him; but whosoever shall speak against the Holy Spirit, it shall not be forgiven him, neither in this age, nor in that which is to come. By cross referencing these two passages, we see that "hath not forgiveness for ever" is related to the expression "shall not be forgiven him, neither in this age, nor in that which is to come." Furthermore, we see that this judgment is describing "eternal judgment." Since we know that the "age to come" refers to "eternity," we see that "eternal judgment" takes place "in eternity." Now, I wrote about the phrase "for ever" in the article Revelation 14:9-11 and Christian Universalism and showed several passages from Scripture where "for ever" meant a "temporary process with everlasting consequences." It is also interesting to note that the phrase translated "for ever" is εἰς τὸν αἰῶνα (eis ton aiona) in the Greek. This can be translated very literally (and perhaps wrongly) as "into the age," which we know would mean "into eternity" because "the age" is "the Age of Messiah." Now, I prefer the idiomatic translation "for ever" because this seems to conform better to actual usage than the very literal translation "into the age." However, I just mention this option because it is interesting.
I realize that the phrases "blasphemy against the Spirit" and "hath not forgiveness for ever" are relevant in discussions dealing with Universalism, but I want to save those topics for a separate article. In this article, my intention has only been to show that the word "eternal" describes something that happens "in eternity."
Some Speculation
As I have mentioned above, I suspect that "eternal punishment" refers to "temporal punishment in eternity that has everlasting consequences." To be more specific, (and again I must qualify this by saying that this is simply my opinion and speculation), I tend to think that the unsaved will enter a "correction facility" upon being judged. This "correction facility" would correspond to the "lake of fire" in Revelation 20. The purpose of the correction facility is to bring the unsaved to salvation through faith in Jesus Christ for eternal life. He already died for their sins (1 John 2:2), but they still lack life. Therefore, they need to believe in Him for eternal life. After believing in Him, I suspect that they will soon after be given glorified bodies and released from the correction facility. However, in this world, serving a prison term has life-long consequences because the corresponding criminal record prevents people from getting jobs, especially in the government, and is also socially stigmatizing. In heaven, I suspect that things will be much the same. People who get saved through the lake of fire will everlastingly have an inferior social status compared to people who get saved on this side of heaven. Once these people are saved, they will be happy and will have eternal life, but they will be unable to enjoy certain highly esteemed privileges, such as having certain jobs and being able to travel to certain places, because of their "criminal record."
What needs to be remembered is that in a kingdom, not everyone can rule. There needs to be plenty of common citizens and foreigners to rule over. I suspect that people who are saved through the lake of fire will correspond to foreign nations and their common citizenry. I also suspect that "worldly Christians" will correspond to the common citizens of heavenly Israel, which will rule over the other nations. Perhaps some of these Christians will also have places of honor and act as nobles and dignitaries in foreign nations. Finally, I think that "mature Christians" will have the highest places of honor in heavenly Israel. The most honored of them will hold high positions of power in heavenly Jerusalem. Wherever they go, they will be treated as kings. Of course, the Father will be the King of kings (after the Son delivers up the kingdom in 1 Corinthians 15:28), the Son will be the Prince of princes, and the Holy Spirit will be ruling in everyone's heart forever and ever to effect a happy ending for all of God's beloved creatures.
Again, I must stress that this is just speculation and my opinion. However, I hope it has been edifying. This is what I wholeheartedly believe. If my opinion changes in any way, I'll be sure to update this article.