第二类切口、不良切口和非常不良切口

摘要：

Keisler和Leth为了研究$ω_1$ -饱和非标准宇宙中超有限时间线的Loeb测度与U-拓扑的关系，引入了第二类割，即坏割和非常坏割.关于是否存在这些削减的问题在那里提出。本文通过证明：（1）在Peano算术的任何非标准模型中都存在第二类割，（2）$\aleph_1$ -同构性质意味着存在坏割，但没有坏割是非常坏的.

英文摘要：

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 $ω_1$-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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