Luke tells us in Acts 18:9-10 that Paul received a vision from the Lord, telling him that he had many people (laos – G2992) in Corinth. The people of God is one of the phrases, pointing to the main theme of the Kingdom of God, which Luke uses in his narrative, and what he means is that God has entered human history to take out a people for his name, and this included both Jews (Acts 13:17) and gentiles (Acts 15:14), whom Paul insists would become one people (Galatian 3:28; Colossians 3:11; cp Ephesians 2:12-15). Luke refers to the people of God only after Paul breaks off fellowship with the synagogue (Acts 18:10; cp. verses-6-7).
Immediately after the return of Silas and Timothy, Luke says that Paul completely devoted himself to the word of God (Acts 18:5); the KJV says “pressed in the spirit”. Luke implies that preaching the word became Paul’s sole occupation at this time, which would indicate that Silas had brought with him a financial gift for Paul from the brethren at Philippi (cp. Philippians 4:15). Paul was encouraged and he became wholly absorbed in preaching the Gospel in contrast to what we find in Acts 18:3. He began testifying, that is witnessing to the Jews, which has an implication of his taking an oath. What Luke appears to be saying is, Paul placed himself under oath that he had seen the resurrected Jesus on the Damascus road. This was Paul’s witness; he couldn’t claim what the Twelve could, namely what is found in the four Gospel narratives. Paul had Damascus; it is there that he met Jesus—the glorified, resurrected Jesus, and it was he whom Paul preached in the synagogue at Corinth.
About the time of Paul’s renewed spirit, there also appeared an organized opposition to his Gospel. Luke uses the word antitassomai (G498). Paul uses this word for those who resist the authority of human government, saying that such authority exists at the ordinance of God and resisting human authority opposes what God has put in place and will ultimately reap the judgment of God (Romans 13:2). According to some scholars, Luke isn’t clear as to what the Jews oppose. Do they oppose God by blaspheming the Way (Jesus), or do they oppose Paul by reviling his testimony—i.e. claiming he hadn’t seen the resurrected Jesus as he claimed? In fact, some translations seem to take this position (NIV, NET, Moffat, Amplified), but others point to their blaspheming (KJV, NASB, ASV). Personally, I believe they simply rejected Paul’s testimony that he had seen the resurrected Jesus. This put Paul under an oath, and later we find him shaving his head (Acts 18:18). If this is not the reason for his vow, then we are completely in the dark as to what Paul’s vow might be. Luke tells us that Paul told the Jews as he left, that their ‘blood’ was upon their own heads, indicating, at least to me, that it was Paul’s personal testimony that was rejected. There is a sense of Paul pointing out that their actions or words were bringing judgment down upon them, and he was innocent of the consequences. But, whichever is factual, blaspheming the Way, or rejecting Paul’s testimony of what he had seen, Paul could no longer remain in the synagogue and expect to be taken seriously.
Immediately upon Paul’s separating himself from the Jews who opposed him, Crispus, the ruler of the synagogue also separated himself from that fellowship and was baptized with his whole household (Acts 18:8). It is then that the Corinthians (read the Jews and gentile God-fearers in the synagogue) believed and were baptized. Luke isn’t clear as to whether they believed on the merits of Paul’s preaching, or if they believed because their leader, Crispus, believed and was baptized. Personally, I think it is the latter. I strongly believe that the leadership of religious communities help or hinder the faith of those they teach. People trust those they believe follow the Lord, and the Lord holds the shepherd of his flock responsible for the people placed under his care (cp. Ezekiel 34:2-6, 11-12, 14-16). It should not be taken lightly that Luke shows Paul enjoyed the unusual success of converting the ruler of the synagogue. This was no small accomplishment.
 Codex D, the Western text, expands on verse-12: “having talked together among themselves against Paul, and laying hands on him, they led him to the proconsul, crying out and saying…”