Accessing An Indirect Table

I have the following table design:

Person
id (pk)
name
city_id (fk)

City
id (pk)
name
country_id (fk)

Country
id (pk)
name

Within Person model:

'city' => array(self::BELONGS_TO, 'City', 'city_id')

Within City model:

'country' => array(self::BELONGS_TO, 'Country', 'country_id')
'people' => array(self::HAS_MANY, 'Person', 'city_id')

Within Country model:

'cities' => array(self::HAS_MANY, 'City', 'country_id')

I want to display the country name from an instance of the Person model using CActiveDataProvider. I believe I need to this by passing a CDbCriteria object. The sql join that I'm trying to create is

select * from person
JOIN city ON person.city_id = city.id
JOIN country on country_id = country.id;

I tried doing this using

$criteria=new CDbCriteria;
$criteria->join  = 'JOIN city ON city_id = city.id';
$criteria->join .= ' JOIN country ON country_id = country.id';

But I get the error

Property "Person.country" is not defined.

I would prefer to not have to create any manual joins and just use relations. Is there any way to extend the relations so that I can access the country name? Is the table design incorrect perhaps?