Large Cardinals for Fun and Profit
Andrew Brooke-Taylor
(Gödel Research Center, University of Vienna)
Abstract:
There are two kinds of unprovable statements in mathematics. There are
those like the continuum hypothesis, that are consistent assuming that
the usual axioms of set theory (ZFC) are; we just can't decide whether
they "should be" "true" or not. Then there are those like "there is a
model of ZFC" that we think are probably true, but which could well be
inconsistent even if the basic system ZFC is consistent.
Of course, being at heart dashing and bold adventurers who laugh in the
face of potential inconsistency, the latter seem much more exciting. I
will give a brief tour of such "large cardinal axioms", how they arise,
and how they can sometimes even be relevant to other areas of
mathematics.