18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |