A.T. Robertson Commentary Romans 4:13

"For not through the law was the promise to Abraham or to his seed that he should be heir of the world, but through the righteousness of faith." — Romans 4:13 (ASV)

That he should be the heir of the world (το κληρονομον αυτον εινα κοσμου). The articular infinitive (το εινα) with the accusative of general reference in loose apposition with η επαγγελια (the promise). But where is that promise? Not just Ge 12:7, but the whole chain of promises about his son, his descendants like the stars in heaven, the Messiah and the blessing to the world through him. In these verses (13-17) Paul employs (Sanday and Headlam) the keywords of his gospel (faith, promise, grace) and arrays them against the current Jewish theology (law, works, merit).