(1) Admits as regular students only individuals having a certificate of graduation from a high school, or the recognized equivalent of such a certificate;
(2) Is legally authorized in this state to provide a program of education beyond high school;
(3) Provides an educational program for which it awards a bachelor's or higher degree, or provides a program which is acceptable for full credit toward such a degree, or provides a program of postgraduate or postdoctoral studies, or provides a program of training to prepare students for gainful employment in a recognized occupation; and
(4) Is a public or other nonprofit institution.
Notwithstanding any of the foregoing provisions of this definition all colleges and universities in this state are institutions of higher education.