PROBLEMAI KONTINUUM

PROBLEMAI KONTINUUM, bo usulhoi nazariyai majmuho isbot kardani masalai ba istiloh kontinuum-farziya meboshad, ki matlaash chunin ast: iqtidori kontinuum avvalin iqtidorest, ki az iqtidori majmui tamomi adadhoi naturali kalon meboshad. Tamimi kontinuum-farziya in tavr ast: ba­roi dar guna majmui R avvalin iqtidori az iqtidori majmui mazkur kalon, iqtidori majmui tamomi zermajmuhoi majmui R ast. Kontinu- um-farziyaro G. Kantor solhoi 80 asri 19 bayon karda bud. Kushishhoi buzurgtarin matematikhoi okhiri asri 19 va avvali asri 20 az jumla iqdomi khudi Kantor ham dar rohi isboti in problema behuda raftand. In yak guruh matematikon (masalan, matematikoni fransavi R. Bar, A. Lebeg, ma­tematiki soveti N. N. Luzin va digar)-ro ba khulosae ovard, ki Problemai kontinuumro bo usulhoi ananavii nazariyai majmuho isbot kardan mumkin nest. Bo yorii sahedtarin usulhoi mantiqi matematiki va nazariyai aksiomatii majmuho durustii in aqida tasdiq gardid. Soli 1936 mate­matik va mantiqshinosi avstriyagi K. Gyodel isbot namud, ki kontinuum-farziyai tamimyofta bo yak sistemai tabiii nazariyai aksioma­tik majmuho hambastagi dorad. Va az in jost, ki onro bo yorii usulhoi ananavi nametavon rad kard. Nihoyat, soli 1963 mantiqshinosi amerikoi P. Koen ba istiloh metodi ijbori ikhtirokardaashro istifoda burda, isbot karda tavonist, ki inkori  Problemai kontinuum niz ba hamin sistemai zikrshuda hambastagi do­rad. Pas, Problemai kontinuumro bo yorii metodhoi muqarrarii nazariyai majmuho isbot kardan mumkin nest. Payravoni P. Koen minbad bo yorii usulhoi ijbor natijahoi bisyore ba dast ovardand, ki to ba andozae mavqei kontinuum-farziya va kontinuum-farziyai umumiyatyoftaro muayyan kardand va aloqamandii onhoro bo digar prinsiphoi nazariyaviyu majmui nishon dodand.

Natijahoi dastovard az on shahodat medihand, ki dar zinai hozirai taraqqiyoti nazariyai majmuho usulhoi gunoguni asosnokkunii in sohai ilm mavjudand.