The church at Antioch was founded after the church of Jerusalem sent Barnabas to Antioch after Jews fleeing to Jewish communities outside the land of Israel due to the severe persecutions. Barnabas brought Saul, the Apostle to the Gentiles to Antioch where they founded the church. The church at Antioch was apostolic and became the launching point to bring the Gospel to many other Gentiles. They founded apostolic churches and ordained the elders to care for the sheep, including at Antioch. The church at Antioch was and remains a Catholic/Orthodox Church, belonging to the holy catholic apostolic church. The church at Antioch appealed to the Apostles and elders at Jerusalem , appointing a delegation led by the Apostle Saul/Paul and Barnabas to get a ruling in the question of whether Gentiles who were granted repentance unto life and were baptized were also required to be circumcised. Paul and Barnabas had said no but apparently that was no definitive enough for Antioch and so it went to all the Apostles who exercised the power of binding and loosing.
Don't neglect to recognize that when Barnabas came, he was sent because the ministry was already there and functioning, planted by several predecessers to Barnabas, and was obviously large, congregational, and non-denominational. Likely they at that time had no church house.
While I don't define "Apostolic church" it appears that the foundational Antioch assembly was already in place, after the style of patterning the local assembly's operation on the prototype model brought from Jerusalem by its former congregants--following the doctrine of the Apostles, breaking bread from house to house, personal and corporate prayer and evangelism, and answering to no one but its Head, the Lord Jesus Christ--as is proper for any genuine local congregation--and not to some other group external to the local assembly.
What have I left out? Oh, yes, and because of their continual occupation was personal evangelism the locals titled the "Christians" just as we title people by their vocation or avocation: pharmacist, musician, butcher, arborist, etc. What I see is them practicing their love of their Savior through the work of their local body with Jesus Christ as its acknowledged head. What I don't see there is anybody named "Catholic," until hundreds of years later, and I do see Peter or Paul finding onlookers literally worshipping them, they stopped it immediately, and so did the Holy Spirit.
Paul did plant churches through himself risking his life and leading men who personally made and baptized enough disciple to form a minyan of believers, committin it to the Lord for its prosperity. not possibly or quite likely refer to one local assembly of God, or at the outside a plurality with the quality distributive to a typical individual church.
. No, the Jerusalem assembly was the type and prototype for each church to come: singular, independent, autonomous, immersionist, founded by the Holy Ghost and conferring church unity on 120 local disciples, with the government by a plurality of elders, having several representative coequal Bible students and speakers, and appointed deacons to be accountable for and oversee the distribution of common resources. It answered to Christ alone for its direction, and appointed no permanent clergy or vicar or Popish clergy with sharp lines drawn, other than that of the original disciple-Apostles. When they were dead, the Apostolic Age was done.
It is my contention that they expected a local assembly of Christ-followers to essentially replicate this model, with each body of Christ to take shape according to its own leading by the Holy Ghost.
In the beginning formative days of Apostles executing their commission (which was to personally make, baptize, and instruct disciples) the application of the doctrine of the Apostles personally received from Jesus their Master and personal supervisor of their progress was being inscripturated. When that work was finished, that of eyewitnesses personally instructed by Jesus and commissioned by Him, the God-breathed content of the New Testament canon was completed. When that completion was accomplished the flow of special revelation was completed, and that which was in part was done away: the gift of prophecies was negated; he practice of tongues ceased of themselves through misuse and lack of relevance; and the Providential exposure of some secret or hidden knowledge by intuition and not deductive discovery disappeared because it was no longer an effective way to accomplish the advancement of the Kingdom by relying on mysterious and arcane ways outside of the plain Word of The Lord.
In none of this did the instrumentality of a supralocal administration, as typified by today's catholicity, play any role in the development of the primitive churches. Their numbers advanced rapidly and broadly through the dynamics of individual evangelism as ordained by the Risen Christ, and not by the ecclesiology established for a theocracy under the Mosaic Law, now over.
Though the social power derived from theistic Platonism can be impressive in magnitude and effect, the concentration of too much carnal power in too few hands sabotoges the entire meaning of the spirit of the Gospel, which is the reliance of the individual on the Might of his Savior alone, and not on dependence on the power of money and/or politics.
In the primitive churches, there was not a hint of practical catholicity employed in planting or growing the local churches. To say otherwise is to grossly overstate the unifying importance of the Apostle-led travelling bands of evangelists. -----------
"Then he answered and spake unto me, saying, This is the word of the LORD unto Zerubbabel, saying, Not by might, nor by power, but by my spirit, saith the LORD of hosts" (Zech. 4:6 AV)
The Holy Ghost is the resurrection power of the prayerful, doctrinally pure independent local church, for the purposes through which its Head, The Lord Jesus Christ, wishes to accomp;lish mighty things in its age and community.
This is not possible under the philosophy and carnality of the catholic system, IMHO.