inaccessible cardinal

In mathematics, a cardinal number k >

\aleph_0

(aleph-null) is called weakly inaccessible, or just inaccessible, if the following two conditions hold.

cf(k) = k, where cf denotes the cofinality. Such a cardinal is called a regular cardinal.
There is no next smaller cardinal number; i.e., for every cardinal l < k, there is another cardinal number between l and k. Such a cardinal number is called a limit cardinal.

Every transfinite cardinal number is either regular or a limit; however, only a rather large cardinal number can be both. In fact, assuming that ZFC is consistent, the existence of inaccessible cardinals provably cannot be proven in ZFC. All inaccessible cardinals are large cardinals. Some inaccessible cardinals may be strongly inaccessible cardinals.

<< Previous

Word Browser

Next >>

fort washington (disambiguation)
frankford
canadian war museum
aelius
weissenberg number
bickley
uss john a. moore (ffg 19)
music of mexico
allen b. dumont
uss antrim (ffg 20)
battle of edington

uss flatley (ffg 21)
oar
rule britannia
uss fahrion (ffg 22)
londonderry air
arthur dee
uss lewis b. puller (ffg 23)
beth two
uss jack williams (ffg 24)
naevius
uss copeland (ffg 25)

goldenrod
fort washington
uss gallery (ffg 26)
pete trewavas
ray wilson (musician)
stingray (tv show)
strongly inaccessible cardinal
mahlo cardinal
norwich city f.c.
black gold
zero sharp

dash mihok
iron vote
yellow dog democrat
klinikum aachen
north petherton
dominic monaghan
totally indescribable cardinal
apple iigs
measurable cardinal
warlords (card game)
strong cardinal