# Difference between revisions of "Upper attic"

From Cantor's Attic

Line 1: | Line 1: | ||

Welcome to the upper attic, where we store all the various large cardinals that are too large to prove to exist in the usual ZFC axioms of set theory. | Welcome to the upper attic, where we store all the various large cardinals that are too large to prove to exist in the usual ZFC axioms of set theory. | ||

− | + | * [[inconsistency]] | |

* [[Reinhardt]] cardinal | * [[Reinhardt]] cardinal | ||

* [[super n-huge]] cardinal | * [[super n-huge]] cardinal | ||

Line 10: | Line 10: | ||

* [[supercompact]] cardinal | * [[supercompact]] cardinal | ||

* [[strongly compact]] cardinal | * [[strongly compact]] cardinal | ||

+ | * [[Woodin]] cardinal | ||

* [[strong]] cardinal | * [[strong]] cardinal | ||

* [[tall]] cardinal | * [[tall]] cardinal |

## Revision as of 06:15, 18 December 2011

Welcome to the upper attic, where we store all the various large cardinals that are too large to prove to exist in the usual ZFC axioms of set theory.

- inconsistency
- Reinhardt cardinal
- super n-huge cardinal
- superhuge cardinal
- huge cardinal
- almost huge cardinal
- extendible cardinal
- supercompact cardinal
- strongly compact cardinal
- Woodin cardinal
- strong cardinal
- tall cardinal
- measurable cardinal
- Ramsey cardinal
- subtle cardinal
- ineffible cardinal
- totally indescribable cardinal
- indescribable cardinal
- weakly compact cardinal
- hyper-Mahlo cardinal
- Mahlo cardinal
- inaccessible cardinal, also known as strongly inaccessible
- weakly inaccessible cardinal
- universe cardinal
- weak universe cardinal
- down to The middle attic