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[RigaMortus2]

I think Core is basically up to what the DM allows and everyone agrees on.

For me personally, I'd say all PHBs, DMGs and MMs are Core, and if you are playing a specific setting (like FR or Eberron) then those books would be "core" for those campaigns. Then again, as DM, I allow just about anything, so my definition of "core" doesn't really affect me and my group anyway. But that's the definition I'd use.