“Employer”:
     (1) a city of more than 500,000 inhabitants;
     (2) the Board of Education of the city, with respect to any of its employees who participate in this Fund;
     (3) the Chicago Housing Authority, with respect to any of its employees who participate in this Fund subject to the provisions of Section 8-230.9;
     (4) the Public Building Commission of the city, with respect to any of its employees who participate in this Fund; and
     (5) the Retirement Board.