structure for 'Mathematics'    |     alphabetical list of themes    |     expand these ideas

6. Mathematics / A. Nature of Mathematics / 4. The Infinite / j. Large cardinals

[types of vast cardinal as set theory ascends]

5 ideas
Very large sets should be studied in an 'if-then' spirit [Putnam]
Infinity has degrees, and large cardinals are the heart of set theory [Maddy]
For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]
An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]