(i) admits as regular students only persons having a certificate of graduation from a school providing secondary education, or the recognized equivalent of such a certificate;

(ii) is legally authorized within the Commonwealth to provide a program of education beyond secondary education;

(iii) provides an educational program for which it awards a bachelor's degree or provides not less than a two-year program which is acceptable for full credit toward such a degree;

(iv) is a public, nonpublic or other nonprofit institution; and

(v) is accredited by a nationally recognized accrediting agency or association or, if not so accredited, is an institution with respect to which the secretary has determined that there is satisfactory assurance, considering the resources available to the institution, the period of time, if any, during which it has operated, the effort it is making to meet accreditation standards, and the purpose for which this determination is being made, that the institution will meet the accreditation standards of such an agency or association within a reasonable time, or is an institution whose credits are accepted, on transfer, by not less than three institutions which are so accredited, for credit on the same basis as if transferred from an institution so accredited.

Such term also includes any school which provides not less than a one-year program of training to prepare students for gainful employment in a recognized occupation and which meets the provisions of subclauses (i), (ii), (iv) and (v). For purposes of this clause, the secretary shall, with the cooperation of the State Board of Education, publish a list of nationally recognized accrediting agencies or associations which he determines to be reliable authority as to the quality of training offered.