People's Dictionary of the Bible
Achaia (a-kâ' yah or a-kä'yah). This was the original name of a district in the northwest of the Peloponnesus: in New Testament times it had a wider signification; for the Roman provinces of Achaia and Macedonia comprehended the whole of Greece. It is in this larger sense that Achaia must be understood. Acts 18:12; Acts 18:27; Acts 19:21; Romans 15:26; Romans 16:5; 1 Corinthians 16:15; 2 Corinthians 1:1; 2 Corinthians 9:2; 2 Corinthians 11:10; 1 Thessalonians 1:7-8. Achaia was first a senatorial province, and had proconsuls. Tiberius changed it into a province imperial under procurators; and Claudius restored it to the senate. Hence Gallio, before whom Paul appeared, was proconsul. Corinth was the capital city.
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Rice, Edwin Wilbur, DD. Entry for 'Achaia'. People's Dictionary of the Bible. https://www.studylight.org/dictionaries/eng/rpd/a/achaia.html. 1893.