samanya upaay

sett siddhant mein, ack samanya upaay ack maapane yogya cardinal κ parr ack upaay haye jaise kii κ maanchitra parr pehchaan kaary kaa samkaksh varg ultrapower nirmaan mein κ key liye. samatulya roop seey, yadi f: κ → κ aisaa haye kii adhikansh α <κ key liye f (α) <α haye, tou ack β <κ aisaa haye kii adhikansh α <κ key liye f (α) = β haye. (yahaan, "adhikansh" kaa arth haye kii κ key tatvon kaa samooh jahan sampatti haye, vaha ultrafilter kaa sadasya haye, i.ee. iska maap 1 haye) bhee samatulya haye, ultrafilter (maap 1 key sett kaa sett) vikarn pratichhedan key tahat bund haye.
ack samanya upaay key liye, κ key kissy bhee bund aseemit (club) upasamuchchay mein κ seey cumm adhikansh ordinal hotey hain. aur κ seey cumm key adhikansh ordinals vaalaa koee bhee upasamuchchay κ mein sthir hotaa haye.
yadi ack anginat cardinal κ parr ack maap haye, tou usa parr ack samanya maap haye.

