# Difference between revisions of "Middle attic"

From Cantor's Attic

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[[File:StAugustineLighthouse.jpg | right | St. Augustine Lighthouse photo by Madrigar]] | [[File:StAugustineLighthouse.jpg | right | St. Augustine Lighthouse photo by Madrigar]] | ||

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+ | Welcome to the middle attic, where you will find many of the commonly used concepts of infinity in set theory. All cardinals here either provably exist or have existence equiconsistent with ZFC. | ||

* Up to the [[upper attic]] | * Up to the [[upper attic]] |

## Revision as of 16:58, 28 December 2011

Welcome to the middle attic, where you will find many of the commonly used concepts of infinity in set theory. All cardinals here either provably exist or have existence equiconsistent with ZFC.

- Up to the upper attic
- the Feferman theory
- $\Sigma_n$-reflecting and the fully reflecting cardinals $V_\delta\prec V$
- $\Sigma_2$ reflecting cardinal
- $\beth$-fixed point
- strong limit cardinal
- the $\beth_\alpha$ hierarchy
- $\aleph$-fixed point
- the $\aleph_\alpha$ hierarchy
- $\aleph_\omega$ and singular cardinals
- the continuum
- regular cardinals
- $\aleph_1$, the first uncountable cardinal
- $\aleph_0$ and the rest of the lower attic