
kripke-pletku settu sidhaantham

soul kripkeyum richard plettum vikasippichedutha oru svayamsidhamaaya settu sidhaanthamaanu kripke-pletku settu sidhaantham (kepi).
eee sidhaantham ekadesham zfc-yude pravachana bhaagamaayi kanakkakkaam, athu athinekkaal valare durbalamaanu. 
svayamsidhangal.
athinte roopeekaranathil, oru δ0 formula ennathu ellah quandifierukalum parimithappedutthiyirikku onnaanu. ithinartham eathu alavum formula _ 1 allengil formula _ 2 aanu (levi shreni kaanuka.)
chilar ennaal ellah rachayithaakkalum ulppedunnilla 
ananthathayodukoodiya kp yeei kpω kondu soochippikkunnu. eee sidhaanthangal keey. pii., saamaanyavalkkaricha aavarthana sidhaanthavum sveekaaryamaaya oordinalukalude sidhaanthavum thammilulla adutha bandhatthilekku nayikkunnu.
svayamsidhaanthangalonnum maattathe, ozhivakkiya madhyathinte niyamam upekshichu keey. pii. yeei oru kriyaathmaka settu sidhaanthamaayi padikkaam.
shoonyamaaya settu.
ananthathayude soothravaakyathil pole eathenkilum settu formula _ 3 nilavilundennu anumanikkappettaal, shoonyamaaya settinte soothravaakyam anaavasyamaanu, kaaranam athu upasett soothravaakyathinu thulyamaanu. koodaathe, prabhaashana prapanchatthil oru amgathinte nilanilpp, athaayath.iii.θx (x = x), phastt-oordar lojikkinte chila formulationukalil soochippikkunnu, eee saahacharyathil shoonyamaaya settinte svayamsidhaantham δ0-seppareshante svayamsidhathayil ninnu pinthudarunnu, athinaal athu anaavasyamaanu.
sermelo-frenkel settu sidhaanthavumaayi thaarathamyam cheyyuka.
soochippichathupole, mukalil paranjava power settu svayamsidham, choys, chilappol anantatha enniva ozhivakkunnathinaal zfc-yekkaal durbalamaanu. ivide verthirikkalinteyum shekharanathinteyum soothravaakyangal zfc-yile anubandha soothravaakyangalekkaal durbalamaanu, kaaranam ivayil upayogikkunna soothravaakyangal φ parimithamaaya alavil maathram parimithappedutthiyirikku.
kpyude pashchaathalatthil inductionte svayamsidhaantham regularityude saadhaarana svayamsidhathayekkaal shakthamaan, ithu oru settinte poorakatthilekku (thannirikkunna settil illaatha ellah settukaludeyum klaas) induction prayogikkunnathinu thulyamaanu.
sidhaanthangal.
sveekaaryamaaya settukal.
α" oru paridhi oordinal aanenkil, "γ" ll ninnu "α" lake oru σ1 (l "α") mapping ulla oru "γ" <"α" nilavilillengil maathrame oordinal "α" sveekaaryamaaya oordinal aakoo. m" ennathu kp yude oru staanderd modalaanengil, "m" leeii oordinalukalude koottam sveekaaryamaaya oru oordinalaanu.
cartician uthppannangal nilavilundu.
sidhaantham
a", "b" enniva settukalaanenkil, "a", "b" ennivayude "a", "b" ennee moolakangalude ellah oordar cheytha jodikalum ("a", "b") ulkkollunna oru settu "a" × "b" undu.
thelivu
a" enna amgamulla singleton settu, {"a"} ennu ezhuthiyirikkunnathu, extensionaalittiyude svayamsidhatha prakaram krameekarikkappedaatha jody {"a", a "} nuu thulyamaanu. 
singleton, settu {"a", "b"}, pinne oordar cheytha jody
ellaam jodiyakkiyaanu nilanilkkunnath.
p" ennathu jodiye ("a", "b") soochippikkunnuvennu prakadippikkunna oru saadhyamaaya δ0-formula formula _ 11 dairkhyameriyathaanu nalkunnathu.
settukalude shekharanathinte rund gattangalaanu inipparayunnathu, thudarnnu verthirikkunnathiloodeyu niyanthranam. ellah phalangalum settu builder notteshan upayogichaanu prakadippikkunnathu.
onnamathaayi, formula 15 nalkukayum formula 16 maayi bandhappett shekharikkukayum cheythaal, formula 17-nte chila superset shekharam anusarichu nilavilundu.
δ0-formula 
verthirikkal vazhi formula _ 19 maathram nilanilkkunnu.
formula _ 20 ennathu jody formula _ 19 nte eee shekharathe soochippikkukayaanenkil, athine savisheshamaakkunna oru δ0-formula
formula _ 16 nalkukayum formula _ 24-maayi bandhappett shekharikkukayum cheyyumbol, formula _ 25-nte chila superset shekharam anusarichu nilavilundu.
aaa avasana formulakku munnil 26 enna formula idumbol settu formula 25 thanne verthirikkunnathiloode nilanilkkunnathayi oraal kandethunnu.
oduvil, aagrahicha
union nilavilundu.
kyu.iii.dii.
lohashaasthram.
batchman-howard oordinalaanu kpω-yude sthiratha shakti nalkunnathu. mostovsky colps lemma polulla settu sidhaanthathile chila pothu sidhaanthangal theliyikkunnathil kepi paraajayappedunnu.