# Difference between revisions of "Middle attic"

From Cantor's Attic

Line 1: | Line 1: | ||

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

− | Welcome to the middle attic, where the familiar uncountable cardinals, proved to exist in set theory, steal us upward in uncountable progression, a reliable steel staircase | + | Welcome to the middle attic, where the familiar uncountable cardinals, proved to exist in set theory, steal us upward in an uncountable structural progression, a reliable steel staircase for mathematics, tempting us towards the dreamt possibilities beyond. |

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

## Revision as of 20:48, 28 December 2011

Welcome to the middle attic, where the familiar uncountable cardinals, proved to exist in set theory, steal us upward in an uncountable structural progression, a reliable steel staircase for mathematics, tempting us towards the dreamt possibilities beyond.

- 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
- the continuum
- $\aleph$-fixed point
- the $\aleph_\alpha$ hierarchy
- $\aleph_\omega$ and singular cardinals
- $\aleph_2$, the second uncountable cardinal
- regular cardinals
- $\aleph_1$, the first uncountable cardinal
- $\aleph_0$ and the rest of the lower attic