Heidegger's Bible Handbook: 1 Corinthians: Title
1. Inscription of the Epistle. Corinth was the most illustrious city of Achaia, abounding in sins. The Church in it was founded by Saint Paul.
This Epistle is inscribed, Παύλου τοῦ Ἀποστόλου ἡ πρὸς Κορινθίους ἐπιστολὴ πρώτη, the first Epistle of the Apostle Paul to the Corinthians. That it was written by Paul, and to the Corinthians, the Epistle itself, 1 Corinthians 1:1, 2, teaches. Now, Corinth was the most celebrated emporiumof all Achaia, very populous and wealthy; situated on the Isthmus between the Ægean and Ionian Seas. Whence Corinth was called bimaris, of two seas, by Ovid. From its riches, on account of which it is called ὀλβία Κόρινθος, blessed/prosperous Corinth, by Pindar, it came to such luxury, softness, and pride, that thence the proverb was born: οὐ παντὸς ἀνδρὸς εἰς Κόρινθόν ἐσθ᾽ ὁ πλοῦς, it does not happen to just any man to visit Corinth. Although others understand this of the difficulty of the Corinthian port. Chrysostom also calls it πόλιν τῶν οὐσῶν καὶ γεγενημένων ἐπαφροδιτάτην, the most charming city of all. Pride had puffed them up unto contempt of the Roman name, and it brought destruction upon them, with Mummius as victor. But to the city, restored by Julius Cæsar, quickly both the opulence and the old vices returned. When Saint Paul had come thither, he converted Crispus and Sosthenes, two prefects of the Jewish Synagogue to Christ, to whom others, both Jews and gentiles, were soon added. Paul, thus remaining for eighteen months at Corinth, Acts 18:11, in this city, although wallowing in luxury and immersed in lusts, planted a flourishing Church, which nevertheless, after his departure, schisms and the old and prevailing sins again began to corrupt and defile.
Heroides, poem XII, line 27. Publius Ovidius Naso (43 BC-17 AD) was a Roman poet. Odes, Olympian XII, line 4. Pindar (522 BC-443 BC) was a lyric poet of Greece, esteemed by some to be the greatest.  Lucius Mummius Achaicus (second century BC) was a Roman statesman and general. Mummius broke the strength of the Achæan League and destroyed Corinth (146 BC).  See Acts 18:8, 17; 1 Corinthians 1:1, 14.