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I started to learn about large cardinals a while ago, and I read that the existence, and even the consistency of the existence of an inaccessible cardinal, i.e. a limit cardinal which is additionally ...

Large cardinal axioms are not provable using usual mathematical tools (developed in $\text{ZFC}$). Their non-existence is consistent with axioms of usual mathematics. It is provable that some of ...

As all probably know, Jack Silver passed away about one month ago. The announcement released, with delay, by European Set Theory Society includes a quote by Solovay about his belief on inconsistency ...

As I understand it, there is a program in set theory to produce an ultimate, canonical model of set theory which, among other things, positively answers the Continuum Hypothesis and various questions ...

The question is essentially what is asked in the title. I split it into two parts (A) (Arguments supporting the existence of large cardinals) What are the main philosophical arguments in defense of ...

Cantor has, in the immortal words of D. Hilbert, given all of us a paradise (or perhaps, I would rather say, a great vacation spot), the TRANSFINITE. $\aleph_0, \aleph_1,\aleph_2\dots$ the lists ...