(1) Admits as regular students only individuals having a certificate of graduation from a high school, or the recognized equivalent of such 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 degree, a program of postgraduate or postdoctoral studies, or 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 subsection, all colleges and universities in this state are institutions of higher education for purposes of this section.