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huge

In mathematics, a cardinal number



κ


{\displaystyle \kappa }

is called huge if there exists an elementary embedding



j
:
V
→
M


{\displaystyle j:V\to M}

from



V


{\displaystyle V}

into a transitive inner model



M


{\displaystyle M}

with critical point



κ


{\displaystyle \kappa }

and









j
(
κ
)


M
⊂
M
.


{\displaystyle {}^{j(\kappa )}M\subset M.}


Here,








α


M


{\displaystyle {}^{\alpha }M}

is the class of all sequences of length



α


{\displaystyle \alpha }

whose elements are in



M


{\displaystyle M}

.
Huge cardinals were introduced by Kenneth Kunen (1978).

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