Climb into Cantor’s Attic, where you will find infinities large and small. We aim to provide a comprehensive resource of information about all notions of mathematical infinity. Our site is organized into several large categories:
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.
Aspiring to the attic, the parlour contains the truly vast finite numbers.
Enjoy the stimulating entertainments of the playroom, full of fun and paradox.
Peruse the selections of our library, the central repository of all references cited here at Cantor’s attic.
Review the foundations of our subject with informative background presentations of ideas used throughout the attic.
Don’t see your favorite large cardinal or ordinal? You can help! We’ve only just begun to build our site, and we welcome knowledgeable expert contributions from the mathematical logic community. Please see the community portal for detailed instructions on how to join our community.