In strict sense, an Arabian either bred by the
Gainey breeding program or consisting entirely of lines descended from the
Gainey program. In looser discussion terms, an Arabian that is a high
percentage of Gainey blood.
I'm not as "up" on the Gainey program as some
others here may be, but Dan Gainey and family utilized a lot of Ferzon breeding,
and their program was well-known in the show ring a few decades back. They
tended to utilize really extreme-headed horses, and also in seeking the rather
stylized "level topline" look, somewhat started the trend toward long, tubular
bodies and flat pelvises. Despite that, they did have some pretty decent
stock that descended from some pretty tough horses, so when one finds Gainey
breeding without those particular traits, it can be pretty respectable riding
stock.