No. The core by defnition, is what is core to the game, the rules that everything else will run off. And I'd hope what is core to most games is included in the PHB, DMG, MM.
PHBII, DMG II, MMII and the books that follow those I'll view in the same light as Unearthed Arcana, Complete Arcane, PHB II (3.5) etcetera.