The BDAG disagrees with your interpretation of it, and AFAIK, it's always used :
ⓐ of the acceptance of the nation of Israel as son of God (
cp. Ex 4:22; Is 1:2
al. where, however, the word
υἱοθ. is lacking; it is found nowhere in the
LXX)
Ro 9:4.
ⓑ of those who believe in Christ and are accepted by God as God’s children (
Iren. 5, 12, 2 [
Harv. II 351, 2]) with full rights
τὴν υἱοθεσίαν ἀπολαβεῖν Gal 4:5; cp.
Eph 1:5. ἡ διʼ αὐτοῦ διδομένη υἱοθεσία AcPl Ha 2, 28 (s.
app.). The Spirit, whom the converts receive, works as
πνεῦμα υἱοθεσίας Ro 8:15 (
opp. πν. δουλείας=such a spirit as is possessed by a slave, not by the son of the house). The believers enter into full enjoyment of their
υἱοθεσία only when the time of fulfillment releases them
fr. the earthly body vs.
23.—Harnack (s.
παλιγγενεσία 2); TWhaling, Adoption:
PTR 21, 1923, 223–35; AWentzel,
Her 65, 1930, 167–76; ADieterich, Eine Mithrasliturgie 1903, 134–56; LMarshall, Challenge of
NT Ethics ’47, 258f; WRossell,
JBL 71, ’52, 233f; DTheron,
EvQ 28, ’56, 6–14; JScott, Adoption as Sons of God ’92. S.
Lampe s.v. υἱοθετέω.—New Docs 3, 17; 4, 173.
DELG s.v.
υἱός.
M-M.
TW.
Sv.
http://www.baptistboard.com/#_ftn21 cp. cp. = compare, freq. in ref. to citation fr. ancient texts
al. al. =alibi (elsewhere), aliter (otherwise), alii (others)
LXX LXX = Septuaginta, ed. ARahlfs, unless otherwise specified—Lists 2, beg.
Iren. Iren. = Irenaeus, Haereses, II a.d.—List 5
Harv. Harv. = WHarvey; s. Iren.—List 5
AcPl Ha AcPl Ha = Acts of Paul, PHamb—List 1
app. app. = appendix, apparatus (when ref. to marginal text-critical information, esp. in N.)
opp. opp. = opposed to, opposite
fr. fr. = from
PTR PTR = Princeton Theological Review—List 6
Her Her = Hermes, Zeitschrift für klassische Philologie—List 6
NT NT = New Testament
JBL JBL = Journal of Biblical Literature—List 6
EvQ EvQ = Evangelical Quarterly—List 6
Lampe Lampe = GL. ed., A Patristic Greek Lexicon—List 6
s.v. s.v. = sub voce (under the word, look up the word)
DELG DELG = PChantraine, Dictionnaire étymologique de la langue grecque—List 6
M-M M-M = JMoulton/GMilligan, Vocabulary of Greek Testament—Lists 4, 6
TW TW = Theologisches Wörterbuch zum NT; tr. GBromiley, Theological Dictionary of the NT—List 6
Sv Sv (at the end of entries)=HSieben, Voces—List 6
http://www.baptistboard.com/#_ftnref21Arndt, William ; Danker, Frederick W. ; Bauer, Walter:
A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago : University of Chicago Press, 2000, S. 1024