Homer uses the terms Achaeans and Danaans (Δαναοί) as a generic term for Greeks in Iliad, and they were probably a part of the Mycenean civilization. The names Achaioi and Danaoi seem to be pre-Dorian belonging to the people who were overthrown. They were forced to the region that later bore the name Achaea after the Dorian invasion. In the 5th century BC, they were redefined as contemporary speakers of Aeolic Greek which was spoken mainly in Thessaly, Boeotia and Lesbos. There are many controversial theories on the origin of the Achaeans. According to one view, the Achaeans were one of the fair-headed tribes of upper Europe, who pressed down over the Alps during the early Iron age (1300 BC) to southern Europe. Another theory suggests that the Peloponnesian Dorians were the Achaeans. These theories are rejected by other scholars who, based on linguistic criteria, suggest that the Achaeans were mainland pre-Dorian Greeks. There is also the theory that there was an Achaean ethnos that migrated from Asia minor to lower Thessaly prior to 2000 BC. Some Hittite texts mention a nation lying to the west called Ahhiyava or Ahhiya. Egyptian documents refer to Ekwesh, one of the groups of sea peoples who attached Egypt during the reign of Merneptah (1213-1203 BCE), who may have been Achaeans.
What was redefined in the 4th century about the people of these names?