
unfoldable cardinal

ganit mein, ack unfoldable cardinal ack nishchit prakaar kii badee cardinal sankhya haye.
aupchaarik roop seey, ack cardinal sankhya κ, λ-unfoldable haye yadi aur kewal tabhi jaba cardinality κ key pratyek transitive model key liye κ, jaise kii κ, "m" mein haye aur "m" mein κ seey cumm lambai key sabhi anukram hotey hain, tou ack gair-tuchchh praathamik antarnihit "m" key "j" koo ack transitive model mein "j" key mahatvapurna bindu key saath κ aur "j" (κ) ≤λ key saath shamil kiya jaataa haye.
ack cardinal koo tabhi ujagar kiya jaa sakata haye jaba yeh sabhi ordinalon key liye λ-unfoldable hoe.
ack cardinal sankhya κ dridhata seey λ-aparivartaniya haye yadi aur kewal tabhi jaba cardinality key pratyek transitive model key liye κ zfc-minus-power sett key liye jaise kii κ "m" mein haye aur "m" mein κ seey cumm lambai key sabhi anukram hain, ack gair-tuchchh praathamik embedding "m" key "j" koo ack transitive model "n" mein ack mahatvapurna bindu key saath "j" honey key saath κ, "j" (κ) ≤λ, aur v (λ) "n" kaa ack subset haye. vyaapaktaa key nuksan key binaa, humm yeh bhee maang curr sakate hain kii "n" mein lambai key sabhi anukram λ shamil houn.
isi tarah, ack cardinal dridhata seey failaane yogya haye yadi aur kewal tabhi jaba yeh sabhi λ key liye dridhata seey λ-unfoldable hoe.
yeye guna anivarya roop seey majboot aur supercompact cardinalon key kamjor sanskaran hain, joe v = l key anuroop hain. inn cardinalon seey sambandhit kaee pramey unake unfoldable yaa dridhata seey unfoldable samkakshon key liye saamaanyikaran karate hain. udaaharan key liye, ack dridhata seey ujagar honey yogya key astitva kaa tatparya uchit bull swayamsiddh key thode kamjor sanskaran kii sthirata seey haye.
ack ramsey cardinal unfoldable haye, aur ell mein dridhata seey unfoldable hoga. haalaanki, yeh v mein dridhata seey prakat honey mein whiffle hoe sakata haye.
l mein, koee bhee unfoldable cardinal dridhata seey unfoldable haye; iss prakaar unfoldable aur dridhata seey unfoldable mein samaan sthirata shakti hoti haye.
ack cardinal key majboot roop seey unfoldable haye, aur κ-unfoldable haye, aggar aur kewal tabhi jaba yeh kamjor roop seey compact hoe. ack κ + ω-unfoldable cardinal poori tarah seey avarnaniya haye aur isase pahale poori tarah seey avarnaniya cardinal kaa ack sthir samooh hotaa haye.