Cantor's Attic

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Descent into History photo by Ernie Reyes

Welcome to Cantor's Attic! Please ascend the stairs into our realm, where you will find yet more staircases ascending to the highest levels of infinity.

The upper attic 
The upper attic is the realm of large cardinals and the higher infinite, extending from inaccessibility to inconsistency.
The middle attic 
The middle attic surveys the infinite cardinals whose existence can be proved in, or is at least equiconsistent with, the ZFC axioms of set theory.
The lower attic 
The lower attic classifies various large countable ordinals.
The parlour 
Aspiring to the attic, the parlour contains the truly vast finite numbers.