▁a ▁universal ▁set . ▁Hence ▁the ▁universe ▁of ▁sets ▁under ▁Z FC ▁is ▁not ▁closed ▁under ▁the ▁elementary ▁operations ▁of ▁the ▁algebra ▁of ▁sets . ▁Un like ▁von ▁Ne umann – B ern ays – G ö del ▁set ▁theory ▁( NB G ) ▁and ▁Mor se – K elle y ▁set ▁theory ▁( M K ), ▁Z FC ▁does ▁not ▁admit ▁the ▁existence ▁of ▁proper ▁classes . ▁A ▁further ▁compar ative ▁weak ness ▁of ▁Z FC ▁is ▁that ▁the ▁ax iom ▁of ▁choice ▁included ▁in ▁Z FC ▁is ▁we aker ▁than ▁the ▁ax iom ▁of ▁global ▁choice ▁included ▁in ▁N B G ▁and ▁M K . ▁ ▁There ▁are ▁numerous ▁mathematical ▁statements ▁und ec id able ▁in ▁Z FC . ▁These ▁include ▁the ▁continu um ▁hypothesis , ▁the ▁White head ▁problem , ▁and ▁the ▁normal ▁Moore ▁space ▁conject ure . ▁Some ▁of ▁these ▁conject ures ▁are ▁prov able ▁with ▁the ▁addition ▁of ▁ax i oms ▁such ▁as ▁Martin ' s ▁ax iom ▁or ▁large ▁cardinal ▁ax i oms ▁to ▁Z FC . ▁ ▁Some ▁others ▁are ▁decided ▁in ▁Z F + AD ▁where ▁AD ▁is ▁the ▁ax iom ▁of ▁determin acy , ▁a ▁strong ▁supp osition ▁in compatible ▁with ▁choice . ▁ ▁One ▁att raction ▁of ▁large ▁cardinal ▁ax i oms ▁is ▁that ▁they ▁enable ▁many ▁results ▁from ▁Z F + AD ▁to ▁be ▁established ▁in ▁Z FC ▁ad jo ined ▁by ▁some ▁large ▁cardinal ▁ax iom ▁( see ▁project ive ▁determin acy ). ▁The ▁M izar ▁system ▁and ▁Met am ath