santript model

ganitiya tark mein, aur vishesh roop seey isake upakshetra model siddhant mein, ack santript model "aim" vaha haye joe apane aakar koo dekhate hue utane hii poorna prakaron koo mahsoos kartaa haye jitna kii "uchit roop seey apekshit" hoe sakata haye. udaaharan key liye, hyperarial kaa ack ultrapower model sootra _ 1-santript haye, jiska arth haye kii aantarik seton key pratyek avrohi nested anukram mein ack gair-khaali pratichhedan hotaa haye.
paribhasha.
maan leejiye kii "κ" ack seemit yaa anant cardinal sankhya hoe aur "m" kuchh pratham-crum bhasha mein ack model hoe. taba "m" koo "κ" kahaa jaataa haye-yadi sabhi upasamuchchay key liye "κ" seey cumm cardinality kaa "a" Â "m", model "m" "a" parr sabhi prakaron koo mahsoos kartaa haye. model "aim" koo santript kahaa jaataa haye yadi yeh haye ."aim".-jahan santript ."aim". m" kii cardinality koo darshaata haye. yaani, yeh aakar seey cumm key maapdandon key sett parr sabhi poorna prakaron koo mahsoos kartaa haye. ."aim".. kuchh lekhakon key anusaar, ack model "m" koo ganana yogya roop seey santript kahaa jaataa haye yadi yeh sootra _ 1-santript haye; yaani, yeh ganana yogya maapdandon key sabhi prakaron koo mahsoos kartaa haye. dusaron key anusaar, yadi yeh ganana yogya aur santript haye tou yeh ganana yogya roop seey santript haye.
prerana.
adhik sahaj dhaarana-kii sabhi poorna prakaar kii bhasha kaa ehsas kiya jaataa haye-bahut kamjor hoe jaati haye (aur ise uchit roop seey kamjor santripti naam diyaa gayaa haye, joe 1-santripti key samaan haye). antar iss tathya mein nihit haye kii kaee sanrachanaon mein aise tatva hotey hain joe paribhaashit naheen hotey hain (udaaharan key liye, r kaa koee bhee divya tatva, shabd kii paribhasha key anusaar, kshetron kii bhasha mein paribhaashit naheen haye). haalaanki, way abhee bhee sanrachana kaa ack hissa hain, isaliye hamein unake saath sambandhon kaa varnan karane key liye prakaron kii aavashyakta haye. iss prakaar humm prakaron kii apani paribhasha mein sanrachana seey maapdandon key sett kii anumati dete hain. yeh tark hamein model kii vishisht visheshtaon parr charcha karane kii anumati detaa haye jinhen humm anyatha yaad curr sakate hain-udaaharan key liye, ack "vishisht" badhate anukram "cn" parr ack baadhya koo usa prakaar koo mahsoos karane key roop mein vyakt kiya jaa sakata haye joe kaee maapdandon kaa upayog kartaa haye. yadi anukram paribhaashit naheen haye, tou sanrachana key baare mein iss tathya koo aadhar bhasha kaa upayog karke varnit naheen kiya jaa sakata haye, isaliye ack kamjor santript sanrachana anukram koo baadhya naheen curr sakati haye, jabaki ack 1-santript sanrachana hogi.
kaaran yeh haye kii hamein kewal aise parameter sett kii aavashyakta hoti haye joe model seey sakhti seey chhote hotey hainh iss pratibandh key binaa, koee bhee anant model santript naheen hotaa haye. ack model "m" parr vichaar karein, aur iss prakaar key pratyek parimit upasamuchchay kaa prakaar (anant) model "m" mein mahsoos kiya jaataa haye, isaliye saghanata seey yeh "m" key saath susangat haye, lekin tuchchh roop seey mahsoos naheen kiya jaataa haye. koee bhee paribhasha joe saarvbhaumik roop seey asantusht haye, bekaar haye; isaliye pratibandh.
udaaharan.
kuchh siddhanton aur mukhyataon key liye santript model maujood hainh
kyu key siddhant aur ganana yogya yaadrichhik graph key siddhant donon koo aage-peechhe vidhi key madhyam seey ω-shrenibaddh dikhaaya jaa sakata haye. ise nimnanusar saamaanyikrit kiya jaa sakata haih ack ganana yogya "κ"-shreneegat siddhant kaa cardinality "κ" kaa anootha model santript haye.
haalaanki, yeh kathan kii pratyek model mein ack santript praathamik vistaar haye, jaid. aff. see. mein saabit naheen hotaa haye. vaastav mein, yeh kathan cardinalon key ack uchit varg key astitva key barabar haye "κ" jaise kii "κ" <"κ" = "κ". baad kii pehchaan kuchh "λ" key barabar haye, yaa "κ" dridhata seey durgam haye.
pramukh models key saath sambandh.
santript model kii dhaarana nimnalikhit tareeke seey pradhaan model kii dhaarana key liye dohri haih maan leejiye kii "tii" ack pratham-crum bhasha mein ack ganana yogya siddhant haye (yaani, usa bhasha mein parasparik roop seey susangat vaakyon kaa ack samooh) aur maan leejiye kii "pee" "tii" kaa ack pradhaan model haye. phir "pee" "tii" key kissy bhee anya model mein ack praathamik embedding koo sweekaar kartaa haye. santript model key liye samatulya dhaarana yeh haye kii "tii" kaa koee bhee "uchit roop seey chhota" model ack santript model mein mool roop seey antarnihit haye, jahaan "uchit roop seey chhota" kaa arth haye cardinality usa model seey badee naheen haye jisamen ise embed kiya jaanaa haye. koee bhee santript model bhee sajaatiya hotaa haye. haalaanki, ganana yogya siddhanton key liye ack advitiya pramukh model haye, santript model aavashyak roop seey ack vishesh cardinality key liye vishisht hain. kuchh nishchit-saiddhaantik dhaaranaon koo dekhate hue, manmaane siddhanton key liye santript model (halanki bahut badee cardinality key) maujood hain. λ"-sthir siddhanton key liye, cardinality key santript model "λ" maujood hain.

