▁its ▁earliest ▁pro ponents ▁and ▁pione ers , ▁and ▁he ▁produced ▁the ▁first ▁book - length ▁treatment ▁of ▁it , ▁The ▁Un prov ability ▁of ▁Cons ist ency , ▁published ▁in ▁ 1 9 7 9 . ▁The ▁solution ▁of ▁a ▁major ▁un sol ved ▁problem ▁some ▁years ▁later ▁led ▁to ▁a ▁new ▁treatment , ▁The ▁Log ic ▁of ▁Prov ability , ▁published ▁in ▁ 1 9 9 3 . ▁The ▁modal - log ical ▁treatment ▁of ▁prov ability ▁helped ▁demonstrate ▁the ▁" int ensional ity " ▁of ▁Gö del ' s ▁Second ▁In comple ten ess ▁Theorem , ▁meaning ▁that ▁the ▁theorem ' s ▁correct ness ▁depends ▁on ▁the ▁precise ▁form ulation ▁of ▁the ▁prov ability ▁predicate . ▁These ▁conditions ▁were ▁first ▁identified ▁by ▁David ▁Hil bert ▁and ▁Paul ▁Bern ays ▁in ▁their ▁Grund lagen ▁der ▁Ar ithmet ik . ▁The ▁unclear ▁status ▁of ▁the ▁Second ▁Theorem ▁was ▁noted ▁for ▁several ▁dec ades ▁by ▁log icians ▁such ▁as ▁Georg ▁Kreis el ▁and ▁Leon ▁Hen kin , ▁who ▁asked ▁whether ▁the ▁formal ▁sentence ▁express ing ▁" This ▁sentence ▁is ▁prov able " ▁( as ▁opposed ▁to ▁the ▁Gö del ▁sentence , ▁" This ▁sentence ▁is ▁not ▁prov able ") ▁was ▁prov able ▁and ▁hence ▁true . ▁Martin ▁Lö b ▁showed ▁Hen kin ' s ▁conject ure ▁to ▁be ▁true , ▁as ▁well ▁as ▁ident ifying ▁an ▁important ▁" ref lection " ▁principle ▁also ▁neat ly ▁cod ified ▁using ▁the ▁modal ▁logical ▁approach . ▁Some ▁of ▁the ▁key ▁prov ability ▁results ▁involving ▁the ▁representation