τὸ κληρονόμον αὐτὸν εἶναι κόσμου … βεβαίαν τὴν ἐπαγγελίαν (4:13–16)

Says 4:13: the promise, ἐπαγγελία (epangelia), to Abraham or his seed, τὸ κληρονόμον (klēronomon, "heir") αὐτὸν εἶναι κόσμου, came not διὰ νόμου but διὰ δικαιοσύνης πίστεως. The articular infinitive states what was promised. Abbott-Smith lists Rom 4:13–14 for κληρονόμος of Abraham.

Uncertain κόσμου. This note leans to the promise of land and of many nations (Gen 12:3; 17:4–6; 22:17–18) widened to the world, as 8:17–23 develops. The alternative is the "many nations" of Gen 17:5 only (4:17–18). The fuller discussion is the Exegete's.

Says 4:14: if the heirs are οἱ ἐκ νόμου, κεκένωται ἡ πίστις καὶ κατήργηται ἡ ἐπαγγελία. Both are perfects: faith "has been emptied" (κενόω; Abbott-Smith, "make empty, vain or of no effect," with Ro 4:14), and the promise "has been nullified" (καταργέω). In 4:15b, where there is no law there is no παράβασις (parabasis, "transgression"), the overstepping of a stated command (compare 2:23; 5:14; on δέ, var.Rom.4.15.de-gar).

Uncertain 4:16 Διὰ τοῦτο ἐκ πίστεως, ἵνα κατὰ χάριν has no verb. This note leans to supplying "the promise is" ("the promise comes by faith," BSB): ἐπαγγελία is the subject of 4:13–14 and returns in εἰς τὸ εἶναι βεβαίαν (bebaian, "sure, guaranteed") τὴν ἐπαγγελίαν. The alternative supplies "the inheritance" or "the heirs are" from 4:14.