Journal of Symbolic Logic

Type Two Cuts, Bad Cuts and Very Bad Cuts

Renling Jin

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Type 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 $\omega_1$-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, (2) the $\aleph_1$-isomorphism property implies that bad cuts exist, but no bad cuts are very bad.

Article information

J. Symbolic Logic, Volume 62, Issue 4 (1997), 1241-1252.

First available in Project Euclid: 6 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]
Secondary: 03H15: Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05] 03C50: Models with special properties (saturated, rigid, etc.)


Jin, Renling. Type Two Cuts, Bad Cuts and Very Bad Cuts. J. Symbolic Logic 62 (1997), no. 4, 1241--1252.

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