You will be assimilated. Resistance is futile!

[Inverse Icarus]

i think culture-borders are on a per-city level. so your new city would have NO CULTURE to start with, and would be pray to the Greek culture, which as weak as it may be is still biger than none.

if you really wanted to rushbuy a temple / library etc to peacefully subvert. go ahead.

[Earthling7]

Something tells me that building a city within the borders of another Civ will not be allowed...

[Dutch]

That is true (as long as you are at peace), but if you found outside his borders, and your cultural borders expand, they might push back his, and perhaps eventually assimiliate his city.