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Type two cuts, bad cuts and very bad cut
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AbstractType two cuts, bad cuts and very bad cuts are introduced in [10] for studying the relationship between Loeb measure and U-topology of a hyperfinite time line in an ω1-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, (2) the ℵ1-isomorphism property implies that bad cuts exist, but no bad cuts are very bad.
Title: Type two cuts, bad cuts and very bad cut
Description:
AbstractType two cuts, bad cuts and very bad cuts are introduced in [10] for studying the relationship between Loeb measure and U-topology of a hyperfinite time line in an ω1-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, (2) the ℵ1-isomorphism property implies that bad cuts exist, but no bad cuts are very bad.
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