How do you define the core?
The core to me are all the muscles and connective tissues that stabilize the body so that the arms and legs (and sometimes neck) can function as we need them to do. These muscles also stabilize the spine in order to do this and to maintain the integrity and health of the spine.
I teach a CEC series on the integration of stability and core development. Check out my website at www.hawaiifitnessacademy.com sometime.