FC ▁is , ▁in ▁fact , ▁consistent ). ▁Hence ▁no ▁statement ▁allowing ▁such ▁a ▁proof ▁can ▁be ▁proved ▁in ▁Z FC . ▁This ▁method ▁can ▁prove ▁that ▁the ▁existence ▁of ▁large ▁card inals ▁is ▁not ▁prov able ▁in ▁Z FC , ▁but ▁cannot ▁prove ▁that ▁assuming ▁such ▁card inals , ▁given ▁Z FC , ▁is ▁free ▁of ▁contradiction . ▁ ▁Pro posed ▁add itions ▁The ▁project ▁to ▁un ify ▁set ▁the or ists ▁behind ▁additional ▁ax i oms ▁to ▁resolve ▁the ▁Cont inu um ▁Hyp oth esis ▁or ▁other ▁meta - math emat ical ▁ambigu ities ▁is ▁sometimes ▁known ▁as ▁" G ö del ' s ▁program ". ▁Mathemat icians ▁currently ▁debate ▁which ▁ax i oms ▁are ▁the ▁most ▁pla us ible ▁or ▁" self - ev ident ", ▁which ▁ax i oms ▁are ▁the ▁most ▁useful ▁in ▁various ▁domains , ▁and ▁about ▁to ▁what ▁degree ▁useful ness ▁should ▁be ▁trad ed ▁off ▁with ▁pla us ibility ; ▁some ▁" mult iverse " ▁set ▁the or ists ▁argue ▁that ▁useful ness ▁should ▁be ▁the ▁sole ▁ult imate ▁criter ion ▁in ▁which ▁ax i oms ▁to ▁custom arily ▁adopt . ▁One ▁school ▁of ▁thought ▁le ans ▁on ▁expand ing ▁the ▁" iter ative " ▁concept ▁of ▁a ▁set ▁to ▁produce ▁a ▁set - the or etic ▁universe ▁with ▁an ▁interesting ▁and ▁complex ▁but ▁reason ably ▁tract able ▁structure ▁by ▁adopt ing ▁forcing ▁ax i oms ; ▁another ▁school ▁advoc ates ▁for ▁a ▁tid ier , ▁less ▁cl utter ed ▁universe , ▁perhaps ▁focused ▁on