Filia Mariae said:
But I'm not really sure from that link how covenant is being defined, or what the essential elements of the covenant are. Can you provide the definition for covenant (from the Reformed perspective)?
Thanks.
If I remember right, a covenant is a formal expression (usually in writing) of a continuing relationship among parties.
The Westminster Confession defines the Covenant of Grace as follows:
... a second, commonly called the covenant of grace; wherein He freely offers unto sinners life and salvation by Jesus Christ; requiring of them faith in Him, that they may be saved, and promising to give unto all those that are ordained unto eternal life His Holy Spirit, to make them willing, and able to believe.
From WCF ch. 7, para. 3
For clarity I'm going to add the sections on the administrations of the Covenant of grace. These are sometimes called "covenants" too, though theologically they're extensions of God's one Covenant of Grace:
"This covenant was differently administered in the time of the law, and in the time of the Gospel: under the law it was administered by promises, prophecies, sacrifices, circumcision, the paschal lamb, and other types and ordinances delivered to the people of the Jews, all foresignifying Christ to come; which were, for that time, sufficient and efficacious, through the operation of the Spirit, to instruct and build up the elect in faith in the promised Messiah, by whom they had full remission of sins, and eternal salvation; and is called the Old Testament.
Under the Gospel, when Christ, the substance, was exhibited, the ordinances in which this covenant is dispensed are the preaching of the Word, and the administration of the sacraments of Baptism and the Lord's Supper: which, though fewer in number, and administered with more simplicity, and less outward glory, yet, in them, it is held forth in more fullness, evidence, and spiritual efficacy, to all nations, both Jews and Gentiles; and is called the New Testament. There are not therefore two covenants of grace, differing in substance, but one and the same, under various dispensations."
WCF ch. 7, para. 5 & 6
'Hope it helps.