Was the Covenant made with the Church or does 'Everlasting' mean something other than 'eternal?' I am posting this question on behalf of another user, and it corresponds to a related textual question.

Galatians 3:16 (KJV) says, 


  "Now to Abraham and his seed were the promises made. He saith not, And
  to seeds, as of many; but as of one, And to thy seed, which is
  Christ."


This appears to be referring to the covenant made in Genesis 17:7. On this basis and others, some have concluded that this covenant was made to 'the Church', as St. Augustine would say, "The Israel of God"; they further cite the passage from Galatians 4:24 where Paul cites two covenants - the covenant at Mt. Sinai "which gendereth to bondage"; therefore, the Covenant w/Israel at Mt. Sinai is "bondage", and the New Covenant, which Paul quotes in Hebrews 8:9 from Jer. 31:33, has 'replaced' the Old Covenant in which they quote Hebrews 8:13 (KJV), "Decayeth and waxeth old is ready to vanish away." They conclude that this covenant indeed passed away in 70 CE, at the Destruction of the Temple at Jerusalem.

The meaning of 'olam' which is clear from the Genesis 17:7 text means 'everlasting', and yet it doesn't describe Heb. 8:13. Are we then to 'assume' that Israel's Covenant with God is not the same 'olam' (everlasting) as Gen. 17:7? Or how else can this be understood?
My answer may not be extensive due to time restraints, but I think it's important to emphasize this main point.

The old covenant (Jer. 31:32), which the Israelites entered into at Sinai (Exo. 24:7), cannot be eternal because it never promised eternal life to the Israelites. Instead of eternal life, God (the other party of the covenant) promised that the Israelites would prolong their days on the earth (Deut. 4:40), that is, in the land of Canaan (Deut. 5:33), if they kept His commandments (i.e., His covenant). Because of their disobedience, the Israelites were exiled on several occasions, with the last exile culminating in the destruction of Jerusalem and the Temple in 70 A.D. by the Roman army. That being said, if the days of the Israelites in Jerusalem were not prolonged...than how much less were they to receive eternal life? Again, the old covenant never promised eternal life.

That being said, there's no wonder why the author of the epistle to the Hebrews (Heb. 8:6) says that Jesus Christ is the mediator of a "better covenant" (κρείττονός διαθήκης) established on "better promises" (κρείττοσιν ἐπαγγελίαις). Among these "better promises" is the promise of "the hope of eternal life, which God, who cannot lie, promised before the world began, but He manifested His word in due times by the preaching" (Tit. 1:2-3) which was committed to the apostles.

The old covenant cannot be eternal because those who enter the covenant are neither immortal nor are they promised immortality. They all must inevitably die (granted, there are one or two exceptions, but let's consider the general rule instead). Also, one should understand that once one party of a conditional, bilateral covenant dies, the entire covenant is rendered void for both parties (see the apostle's example of the marriage covenant in Rom. 7:2-3). Thus, whenever an Israelite dies, he is no longer a party to the old covenant; the old covenant is nullified with respect to him.

On the other hand, while those entering into the new covenant are mortal, they are promised eternal life upon their entrance into the covenant. Thus, the covenant endures eternally because the parties of the covenant, whether Jesus Christ or those who believe in, are or shall be immortal (possessing eternal life). On the one hand, they are promised eternal life by resurrection from the dead. But, on the other hand, all those who believe in Christ live with him (Rom. 6:8).