Looking for obscure SF novel from the 70’s or 80’s

[Aos]

First off, hello.

I’m looking for a SF book. I can neither remember the title or author.
Details.
published in later 70’s or early 80’s
Post apocalyptic far future
City underground with strict caste system based (maybe) on occupation. Castes are named after maybe greek letters or gods (I may remember a character who was part of the Ares Caste)
High tech: one of the main characters has something like an apple watch/baby sitter he wears.
There’s an old semi-immortal guy living on the desolate surface and he owns a three legged dog, which is also semi-immortal.
Possibly a blue cover, looking up at a spaceship blocking out the sky- like everything else I’m fuzzy on this.
might be part of a series.
thank you

 

[PaulMmn]

The following is a synopsis of a story which may have nothing to do with the story being looked for. But the old guy and his dog rang a bell... I think.

Was the city slowly expanding in the direction of the old guy's house, which the expansion planners were upset about, because there wasn't supposed to be a house in the route of expansion?

The old guy was one of the original pilots of the ship that brought the colonists, and had been awarded the right to pick a spot for his house-- which he carefully placed along the path of expansion. He wanted to force the colony to break out of the carefully planned expansion, and thought that the expansion running into his house would cause that break. It did.

He eventually allowed the expansion to move his house-- and they didn't even have to touch his root cellar.

 

[Aos]

I’m not sure. I read this thing do long ago. That one sounds cool, though. Thanks.

 

[Toby Frost]

The caste system bit sounds quite a lot like Brave New World, where people were artificially grown to different requirements (Alpha to Epsilon, I think), but the old guy with the dog doesn't ring any bells.