I understand that it is not clear that hell is eternal or everlasting, but where in the Bible do we unambiguously learn that God AND heaven are necessarily :
a.) eternal OR
b.) everlasting?
These are characteristics indicated by far more than the use of a particular adjective (or adjectival phrase) in the scriptures.
(I am going to set aside discussion of whether “heaven” is supposed to be eternal and/or everlasting, since “heaven” has numerous uses in the scriptures ranging from the heavens of physical nature, to the spiritual abode of supernatural entities less than God, to the world of the resurrection in the Day of the Lord to come, to the state of reality in-or-as which God exists, to a polite indirect euphamism for God Himself.)
I can provide scriptural references for the following, if necessary, but it would take a while to list them, and the basic claims are familiar to most everyone.
1.) God is self-existently alive (“I AM THAT I AM” being the name unique to God alone, usually abbreviated as I AM), the one and only Living God, Who is essentially Life in Himself.
2.) All other things are created and sustained by God. It is for God that all things exist, and from God all things come into existence, and in God all things continue to hold together.
Consequently, even if God can, technically, choose to cease to exist, actually doing so would wipe out all other existence, too, including what we call our past, present and future. None of us would be around now to talk about it. 
3.) God is occasionally (in Isaiah, and in RevJohn) called the First and the Last, or the Alpha and the Omega, or the Beginning and the End. These phrases are marshaled as ways of describing God’s uniquely sovereign status and completeness compared to things which do have beginnings and endings (Isaiah 44:6, “I am the first and I am the last and there is no God beside Me!”); they are not deployed as testimony that God Himself has a finite beginning or end. Notably, these statements (from God about Himself) are often combined with statements of self-existence. (Isaiah 41:4, “I YHWH am the first and with the last I am He!” Rev 1:8, “I am the Alpha and the Omega, Who is and Who was and Who is to come, the Almighty!” Jesus explicitly makes this same claim at Rev 1:17-18, “Do not be afraid, I am the first and the last, and the Living One.” He may have become dead (v.18), but that doesn’t stop Him from claiming this uniquely eternal characteristic of God.)
Compare also with Isaiah 43:10, “I am He!–Before Me there was no God formed, and there will be none after Me!”
4.) God’s status compared to creation is sometimes emphasized in terms of His uniquely ongoing self-existence. Psalm 102:25 declares that YHWH in the beginning did lay the foundation of the earth and create the heavens, which will wear out and perish like old clothes, but YHWH will be remaining unchanged and the same–His years shall never come to an end. (The Hebraist, in his Epistle, quotes this Psalm to describe Jesus the Son as this uniquely self-existent YHWH. Heb 1:10-12.)
There are some other things of this sort–and note that the New Testament texts have these characteristics applied to the Son Himself, personally, as well as to the Father, despite insisting not only on sole monotheism but also on the real distinction of the persons of the Father and the Son. (Also to the Spirit, although most theologians have not tried to deny that the Holy Spirit is fully and uniquely the one true God.)
Thanks for above reply. It is very helpful. Allow me to restate part of my question:
Where in the Bible do we unambiguously learn, or how may we unambiguously deduce, that the final spiritual abode of all those trusting in Christ is necessarily everlasting?
If it’s the ‘final’ abode of people who trust in Christ, wouldn’t that necessitate that it is everlasting? Or are you looking at the idea that could come an end to the existance of the people themselves?
Does this fit what you’re looking for?
"The last enemy to be destroyed is death…For the trumpet will sound, and the dead will be raised imperishable, and we shall be changed. For this perishable body must put on the imperishable, and this mortal body must put on immortality. When the perishable puts on the imperishable, and the mortal puts on immortality, then shall come to pass the saying that is written: “Death is swallowed up in victory.” 1 Cor 15
Sonia
This is typically inferred from:
1.) the statements of God’s eventual fully triumphant victory, in relation to those He has saved from rebellion against Him;
2.) the concept of the Day of the Lord to come being the final day and one of rest–although “nesting fulfillments” of this Day of the Lord should also be kept in mind, i.e. in one sense the final Day of the Lord began with the coming of the Messiah, in another sense it began with the start of the Messiah’s ministry, in another sense it began with the resurrection of the Messiah, in another sense it began with the Ascension of the Messiah, in another sense it began at Pentacost with the authoritative descent of the Spirit, in another sense it began with the overthrow of Jerusalem forty years later, in another sense it will begin with the triumphant return of Christ and the end of tribulation against His earthly followers, in another sense it will finally begin after the Son presents all persons in submission to the Father in parallel with His submission to the Father. (Compare to the theme in all four Gospels of the kingdom being already but not yet present; itself an example of a set of common Biblical already/not-yet themes.)
3.) related to the above, a promise of a final and extensively overarching peace of God (Ya-Ru-Shalom, the name of Jerusalem itself); for example the famous promise at the end of Isaiah 65, where typical ravening enemies shall become peaceful with their prey.
(For universalists, we notice that Isaiah 65:25 exemplifies the final fate of “the serpent”, who shall eat dust for food. That’s a callback to the first prophetic statement from God regarding the defeat of “the serpent” who tempted Adam and Eve, which later texts both OT and NT portray as the greatest spiritual rebel against God. Genesis 3:14 regards this as a curse and punishment, but Isaiah 65 reveals that this is a prophecy of the final peace of “the serpent”!–which, along with the other examples, shall do no evil or harm to anyone in God’s holy mountain on the day of God’s final salvation. Presumably the serpent, humiliated to eating dust, shall follow the lead of “the little child” as well. 
)
There are other final-peace notions in the Bible, of course.
4.) Christ’s message to the church of Philadelphia, Rev 3:12, where “those who overcome” shall become pillars in the temple of “My God”; one translation or interpretation involves him who overcomes never going out from the temple anymore. But the “he” who does not go out might be “My God”, which would fit a bunch of OT contexts and promises, as well as the end of RevJohn. However, insofar as the new Temple will be the congregation of those loyal to God (also a major theme, including especially at the end of RevJohn), then the implication would still be that God shall never depart from those believers again–which by implication means they shall never be sinning again in rebellion against Him.
While I think ultimately the scriptures testify to a successful final reconciliation of at least some of God’s enemies (I would say a successful final reconciliation of all God’s enemies), I try to be pretty flexible about the real possibility of rebellion continuing on for any particular creature up to a point; not even counting the real possibility of new rebellions starting among creations of God still to come. But it may also be true that in the natural history of all God’s creation, in this and any other created universe, rebellion against God occupies only a small (and increasingly smaller) swatch of any of that history.
I wanted to add that how universalists interpret this notion depends on whether a universalist recognizes the existence of rebel spiritual creatures other than mankind, or not. Some kaths do (including myself); others see this as standing for abstract powers or poetically describing merely natural inclinations. We have some of each kind of interpreter here on the forum.
Thanks for the help. Mr. Pratt , what are you referring to with the word “kaths” in your previous post?
Just a nickname of mine for universalists (which in Greek would be something like ‘katholikoi’). Roman Catholics are, doctrinally, not universalists, but they consider themselves the universal or fullest congregation, so they use that term for that purpose. Ironically, the Eastern Orthodox, who also entitle themselves Catholic, have a bit more claim to that term since universalism is a live theological option among them. (But not universally so. Rimshot! 
)
Anyway, I’m in the habit of affectionately abbreviating the three notional options of salvation logic (or ‘soteriology’) among Christians, whether Protestant, RCC, EOx, or otherwise (there are a few others, too), as Calv (for Calvinistic) Arm (for Arminianistic) and Kath (for Katholic, or Universalistic). I don’t mean anything pro or con by the abbreviations; it’s only a handy way to talk and type.
Broadly speaking (aside from variations within categories):
Calv == God intends and acts to save only some sinners from sin, but persists in saving those to completion.
Arm == God intends and acts to save all sinners from sin, but doesn’t persist in saving some sinners to completion.
Kath == God intends and acts to save all sinners from sin, and persists in saving those to completion.
The fourth categorical option would be that God intends and acts to save no sinners from sin, in which case there would obviously be no persistence in saving any sinners as well. But I would be very astonished to find any Christian who believes this. 
(Maybe a Buddhist “Christian”? Do the so-called “Unitarian Universalists”, not to be confused with doctrinal unitarian Christians, consider themselves Christian in any meaningful way?–or think in terms of salvation from sin? I rather doubt it.)
Strictly speaking, Kath soteriology doesn’t necessarily have to involve God being successful in saving all sinners from sin, so long as God keeps persistently acting toward that goal, without giving up or stopping for any reason. But most of us (myself included) go the route of Calvinists (and Arminians, too!) on this topic, and trust God to succeed in what He insists on persisting at.
But if that is the meaning of these phrases, does that imply that everything but God (every creature, every soul) has an end (and God alone is left, as He was in the beginning)?
The following is a passage which clearly affirms that God is everlasting:
The Greek word “αιδιος”, here translated as “eternal” does, in fact, have the meaning of “everlasting”.
But isn’t that word used in Jude 6 (where most universalists would say it doesn’t “everlasting,” and where the context seems to limit it “unto the judgement of the great day”)?
Yes, Michael, that is true. I have often pondered this. I tried to explain it by emphasizing that it was the “chains” that were everlasting, and not the reservation of the angels in those chains.
However, I am not entirely satisfied with this explanation. The book of Jude itself is questionable. It was not accepted even as late as 324 A.D. by Eusebius of Caesarea. As far as I know it was not accepted earlier than that date by anyone except those who wrote the Muratorian fragment. The author of the book of Jude considered the Book of Enoch to have been written by the ancient Enoch mentioned in Genesis. But this is known not to be true.
I have argued elsewhere (in line with Knoch if I recall correctly) that AIDIOS actually means “unseen”, which fits the context of both the Romans and the Jude passages well enough. (And so should be punctuated accordingly in Greek miniscule.)
It could be a double-meaning pun, too, in one or both places. (ai-dios and a-idios) I would be hesitant to ascribe “everlasting” to unseen chains in a sense parallel to God the Unseen, though!
No, the context very clearly excludes that. It’s only a colloquial way of saying that nothing exists that’s greater than God. (In which ultimate and unique ontological greatness, John includes Jesus Christ while still distinguishing between the persons of the Father and the Son. )
Thank you.