The retirement board shall determine the eligibility of officers, employees, and their dependents to participation in the system and shall be the sole authority and judge under such ordinances as may be adopted by the board as to the conditions under which persons may be admitted to and continue to receive benefits of any sort under the retirement system, and may modify allowances for service and disability. The determination of the retirement board shall be final and conclusive and shall not be modified or set aside except for fraud or abuse of discretion.