Sec. 4. INELIGIBLE INDIVIDUALS. Notwithstanding any other provision of this Act, the following employees of the city or of the pension system are not eligible to become members of the pension system:

(1) persons on quasi-legislative, quasi-judicial, and advisory pension boards and commissions;

(2) part-time employees, as defined by the city, other than elected officials whose service is made part-time by law or charter;

(3) seasonal employees;

(4) independent contractors, including consultants; and

(5) employees in positions covered by any other pension plan of the city to which the city contributes, including employees who are excluded from membership in another pension plan by action of the board of trustees of the other pension plan, except to the extent that they are covered in another pension plan only as a beneficiary.