Combat Effects on Cities

[Brutus66]

This is probably a question asked before, but I couldn't find it here in the forum or in the game manual.
What, exactly, happens to a city and its inhabitants when a city is attacked?
Specifically, when does the population get decreased? I thought everytime a city was captured, the population went down by 1, but I have captured size 1 cities without having them being destroyed.
Do buildings only get destroyed during bombardment? Can wonders be destroyed this way?
TIA

[Yosho]

The manual says that size one cities with no culture" get destroyed when taken, so I assume that if a city is size 1 but has some culture, it does not get destroyed.

This also seems to work in such a way that if you have some culture in a city, the AI takes it, and you take it back, it's not destroyed even though the AI didn't have any culture in the city, just so long as you (or perhaps someone else? not sure about that one) has some culture there.

[Guardian]

I think the computer runs a "kill check" on each building in the city to determine whether or not it survives, but I'm not sure if this happens when you bombard/attack the city or only when you actually capture it. I think the manual and/or the Civilopedia says something about this, but I don't have access to either at the moment.

Also, I believe that - like in Civ III - cultural buildings are always destroyed when a city is taken.

Wonders, on the other hand, are never destroyed unless someone actually razes the entire city. Even nukes will never destroy a wonder.

[Solver]

The manual is wrong about city auto-raze. In fact, it is cities that have never exceeded the size of 1 that are auto-razed. If you capture a size 1 city and it doesn't get destroyed, it means the city has, at some point, had a population of 2 or higher.

[Brutus66]

Thanks for the informative responses.