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1.
A group of sororities at the University of Texas in Austin. The sororities include Delta Gamma, Alpha Chi Omega, Alpha Delta Pi and Alpha Phi.
I'm a legacy to one of the Core 4--I hope I get in!
by srattymcintosh August 11, 2013
 
2.
the most elite secret organization, containing only 4 members and multiple associates and associate chicks
Would you like to become an Associate of the Core 4?
by M White Balls October 08, 2004