Thank you for that information
That interpretation seems to be effectively what the branch theory states- That the one true church exists now in several branches, all of which are equally apostolic. I don't buy into that theory, because I believe the natural sate of the church is as one entity. Although I suppose what being "one entity" implies is up to interpretation.
And yet all Persons of God are equally God.
But one cannot be a bishop in the Catholic Church without going through the proper process or without being in communion with Rome. Also, it just says that where Christ is, there is the Catholic Church, not where the bishop is.
I understand this, but it assumes that it was always the case. Ignatius as far as I can see never says "Everywhere there is a Bishop under the Pope... there is the Catholic church"
But I would think that the modern view is inconsistant with Ignatius' other writings viz;
In Smyrneans 8 he says do nothing without the bishop.
Trallians 3 (The structure of the church has no place above Bishop)
Trallians 7 (The bishop holds all power)
Quite specifically he states that there's no Bishop of Bishops in Trallians 3...
"In like manner, let all reverence the deacons as an appointment of Jesus Christ, and the bishop as Jesus Christ, who is the Son of the Father, and the presbyters as the Sanhedrim of God, and assembly of the apostles.
Apart from these, there is no Church."
In the same Epistle...
"For, since ye are subject to the bishop as to Jesus Christ"
(Ibid.) Chapter II
"Be on your guard, therefore, against such persons. And this will be the case with you if you are not puffed up, and continue in intimate union with Jesus Christ our God, and the bishop, and the enactments of the apostles. He that is within the altar is pure, but he that is without is not pure; that is, he who does anything apart from the bishop, and presbytery, and deacons, such a man is not pure in his conscience..."
"For what is the bishop but one who beyond all others possesses all power and authority, so far as it is possible for a man to possess it, who according to his ability has been made an imitator of the Christ Of God?"
(Ibid.) Chapter VII
There is no reference to a bishop having any power derived from communion with a single bishop in Rome - not as far as I can see.
To the Philadelphians he says
"Let governors be obedient to Caesar; soldiers to those that command them; deacons to the presbyters, as to high-priests; the presbyters, and deacons, and the rest of the clergy, together with all the people, and the soldiers, and the governors, and Caesar [himself], to the bishop; the bishop to Christ, even as Christ to the Father. And thus unity is preserved throughout"
Chapter IV
Note bishop to Christ, not bishop to Christ through Pope - Christ's vicar.