My question is about expressions of the form "A of B" when uniqueness of A is guaranteed. Are the following four sentences all okay?

> 
> 1. "Is ABC **a** capital of **a** country in South
>  America?"
> 2. "Is ABC **a** capital of **some** country in
>  South America?"
> 3. "Is ABC **the** capital of **a** country in South
>  America?"
> 4. "Is ABC **the** capital of **some** country in
>  South America?"
> 
> 
> 

I suspect 3 and 4 are okay because there can be only one capital for each country. On the other hand, I suspect 1 and 2 are okay because there are many cities which can be said to be a capital of a South American country.