Eridanus is a constellation. Thus, "Alpha Eridani I" would mean "the first planet of the first star in Eridanus." I do not know that there is such a planet but I understand that this would be the correct terminology. So what does "02 Eridani A II" mean? (See Poul Anderson, David Falkayn: Star Trader, p. 224.) I have found a reference to 02 Eridani B but do not understand it. In any case, 02 Eridani A II is a planet named Ta-chih-chien-pih by its inhabitants and Cynthia by human beings.
Chee Lan from Cynthia remembers "...warm ruddy sunlight and rustling leaves around treetop homes..." (pp. 224-225) We see a Cynthian colony on another planet in The Game Of Empire. These details about Cynthia come immediately after the details about the Merseian city of Ardaig in "Day of Burning."
"Poul Anderson immerses you in the future....Anderson puts you into a whole new world."
-Larry Niven, quoted on the back cover of David Falkayn: Star Trader.
This is an accurate account of Anderson's achievement and I would add that Anderson immerses us more effectively even than Robert Heinlein did.