We sort out to a large extent when a (first order complete theory) T has a superlimit model in a cardinal λ. Also we deal with related notions of being limit.
Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
Department of Mathematics, Hill Center - Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, U.S.A.