Fausset's Bible Dictionary
In New Testament, a Roman province, including the whole Peloponnese, and most of Hellas proper, with the islands. This province, with Macedonia, comprehended all Greece (Acts 18:12; Acts 19:21). The name was given by the Romans, when they took Corinth and destroyed the Achaian League (146 D.C.), which, beginning with the narrow northern region of the Peloponnese called Achaia, afterward included several Grecian states. In Acts 18:12 Gallio, with the minute propriety that marks historical truth, called "deputy" (proconsul). Achaia had only just been restored under Claudius to the senate, whose representatives in the provinces were proconsuls, from having been an imperial province under Tiberius, whose representatives were procurators.
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Fausset, Andrew R. Entry for 'Achaia'. Fausset's Bible Dictionary. https://www.studylight.org/dictionaries/eng/fbd/a/achaia.html. 1949.