Huge Cardinal - Consistency Strength

Consistency Strength

The cardinals are arranged in order of increasing consistency strength as follows:

  • almost n-huge
  • super almost n-huge
  • n-huge
  • super n-huge
  • almost n+1-huge

The consistency of a huge cardinal implies the consistency of a supercompact cardinal, nevertheless, the least huge cardinal is smaller than the least supercompact cardinal (assuming both exist).

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