By definition (the definition I use, at least!), the classes in the Player's Handbook 1 ARE the core classes. All others, from any other source, are extra. The core game consists of the content and rules from the core 3 books - Player's Handbook, Dungeon Master Guide, and Monster Manual - and everything else afterwards is additional content.

Is it just because the PH1 doesn't include some classes that people traditionally think of as core? Bards, Sorcerers, Monks? I suppose, but then again, this is a different game. There is no reason to expect that it would or should have the exact same starting set.