A
cardinal number κ > א
0 is called
Mahlo iff the
set U = {λ < κ: λ is
inaccessible} is
stationary[?] in κ. Assuming that
ZFC is
consistent, the existence of Mahlo cardinals
provably cannot be proved in ZFC.
Mahlo cardinals were first described in 1911 by mathematician Paul Mahlo[?].