TYPE-2 CUTS, BAD CUTS AND VERY BAD CUTS

Type two cuts, bad cuts and very bad cuts are introduced in [10] for s tudying the relationship between Loeb measure and U-topology of a hype rfinite time line in an omega(1)-saturated nonstandard universe. The q uestions concerning the existence of those cuts are asked there. In th is paper we answer, fully or partially, some of those questions by sho wing that: (1) type two cuts exist, (2) the N-1-isomorphism property i mplies that bad cuts exist, but no bad cuts are very bad.