  Type two cuts, bad cuts and very bad cuts are introduced by Keisler and Leth
for studying the relationship between Loeb measure and U-topology of a
hyperfinite time line in an $\omega_1$-saturated nonstandard universe. The
questions concerning the existence of those cuts are asked there. In this paper
we answer, fully or partially, some of those questions by showing that: (1)
type two cuts exist in any nonstandard model of Peano Arithmetic, (2) the
$\aleph_1$-isomorphism property implies that bad cuts exist, but no bad cuts
are very bad.
