You are kidding, right? The word is τεταγμενοι which is a perfect, passive, participle.
Charles Ellicott, Greek Scholar
"The
quasi-middle force of the passive form of the verb is seen in the Greek of Act_20:13, where a compound form of it is rightly rendered “for so he had appointed,” and might have been translated for so he was disposed. It lies in the nature of the case that belief was followed by a public profession of faith, but the word “believed” does not, as some have said, involve such a profession."
Cambridge Greek Testament
"καὶ ἐπίστευσαν ὅσοι ἦσαν τεταγμένοι εἰς ζωὴν αἰώνιον, and as many as were ordained unto eternal life believed. In the controversies on predestination and election this sentence has constantly been brought forward.
But it is manifestly unfair to take a sentence out of its context, and interpret it as if it stood alone. In Act_13:46 we are told that the Jews had adjudged themselves unworthy of eternal life, and all that is meant by the words in this verse is the opposite of that expression. The Jews were acting so as to proclaim themselves unworthy; the Gentiles were making manifest their desire to be deemed worthy. The two sections were like opposing troops, ranged (τεταγμένοι = marshalled) by themselves, and to some degree, though not unalterably, looked upon as so arranged by God on different sides. Thus the Gentiles were ordering themselves, and were ordered unto eternal life. The text says no word to warrant us in thinking that none could henceforth change sides."
Henry Alford, Greek Scholar
"τεταγμένοι]
The meaning of this word must be determined by the context. The Jews had judged themselves unworthy of eternal life: the Gentiles, as many as were disposed to eternal life, believed. By whom so disposed, is not here declared: nor need the word be in this place further particularized. We know, that it is GOD who worketh in us the will to believe, and that the preparation of the heart is of Him: but to find in this text pre-ordination to life asserted, is to force both the word and the context to a meaning which they do not contain."
Expositors Greek Testament
"Act_13:48. ἐδόξ. τὸν λ. τοῦ Κ.: δοξ. τὸν Θ.; frequent in Luke and Paul, cf. 2Th_3:1 for the nearest approach to the exact phrase here.—ὅσοι ἦσαν τεταγ.:
there is no countenance here for the absolutum decretum of the Calvinists, since Act_13:46 had already shown that the Jews had acted through their own choice. The words are really nothing more than a corollary of St. Paul’s ἀναγκαῖον: the Jews as a nation had been ordained to eternal life—they had rejected this election—but those who believed amongst the Gentiles were equally ordained by God to eternal life, and it was in accordance with His divine appointment that the Apostles had turned to them.
Some take the word as if middle, not passive: “as many as had set themselves unto eternal life,” and in support of this Rendall refers to 1Co_16:15, ἔταξαν ἑαυτοὺς (see also Blass, in loco). The rendering here given by Rendall may be adopted without pressing the military metaphor in the verb, as has sometimes been done;"
A T Robertson, Greek Scholar
"
As many as were ordained to eternal life (
hosoi êsan tetagmenoi eis zôên aiônion). Periphrastic past perfect passive indicative of
tassô, a military term to place in orderly arrangement. The word "ordain" is not the best translation here. "Appointed," as Hackett shows, is better. The Jews here had
voluntarily rejected the word of God. On the other side were those Gentiles who
gladly accepted what the Jews had rejected, not all the Gentiles. Why these Gentiles here ranged themselves on God's side as opposed to the Jews Luke does not tell us. This verse does not solve the vexed problem of divine sovereignty and human free agency.
There is no evidence that Luke had in mind an absolutum decretum of personal salvation. Paul had shown that God's plan extended to and included Gentiles. Certainly the Spirit of God does move upon the human heart
to which some respond, as here, while others push him away"
ONLY those who are of the Calvinistic or Reformed theological position, would seriously use this passage to prove "election to salvation", when the CONTEXT, with the
rejecting Jews, and
accepting Gentiles clearly shows otherwise!