ⓘ Huge cardinal. In mathematics, a cardinal number κ is called huge if there exists an elementary embedding j: V → M from V into a transitive inner model M with c ..

                                     

ⓘ Huge cardinal

In mathematics, a cardinal number κ is called huge if there exists an elementary embedding j: V → M from V into a transitive inner model M with critical point κ and

j κ M ⊂ M. {\displaystyle {}^{j\kappa}M\subset M.\!}

Here, α M is the class of all sequences of length α whose elements are in M.

Huge cardinals were introduced by Kenneth Kunen 1978.

                                     

1. Variants

In what follows, j n refers to the n -th iterate of the elementary embedding j, that is, j composed with itself n times, for a finite ordinal n. Also,

                                     
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