Type Two Cuts, Bad Cuts and Very Bad Cuts

Details Type Two Cuts, Bad Cuts and Very Bad Cuts Type Two Cuts, Bad Cuts and Very Bad Cuts

1996-04-24

arxiv.org/abs/math/9604210v1

Mathematics

Logic

Scientific paper

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.

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