The rights and benefits provided under article 18 and covered by this Part are applicable to members of public retirement systems of the State. However, article 18 does not permit any transfer to or from a New York City system and does not allow granting of retroactive membership or credit based on New York City service (whether or not this service is ordinarily covered by the New York State and Local Employees' Retirement System) unless such city adopts article 18 in its entirety. If the City of New York adopts article 18, the New York City Employees' Retirement System, the New York City Teachers' Retirement System, the New York City Police Pension Fund, the New York City Fire Department Pension Fund and the New York City Board of Education Retirement System will then be considered “public retirement systems” for the purposes of article 18.