The PCF Trichotomy Theorem does not hold for short sequences

Menachem Kojman; Saharon Shelah

doi:10.1007/s001530050143

The PCF Trichotomy Theorem does not hold for short sequences

Menachem Kojman, Saharon Shelah

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite κ modulo some ideal I. If a <_I-increasing sequence of ordinal functions has regular length which is larger than κ⁺, then by the Trichotomy Theorem the sequence satisfies one of three structural conditions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length κ⁺. It is shown that this is not the case.

Original language	English
Pages (from-to)	213-218
Number of pages	6
Journal	Archive for Mathematical Logic
Volume	39
Issue number	3
DOIs	https://doi.org/10.1007/s001530050143
State	Published - 1 Jan 2000

ASJC Scopus subject areas

Philosophy
Logic

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abstract = "The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite κ modulo some ideal I. If a <I-increasing sequence of ordinal functions has regular length which is larger than κ+, then by the Trichotomy Theorem the sequence satisfies one of three structural conditions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length κ+. It is shown that this is not the case.",

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AB - The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite κ modulo some ideal I. If a <I-increasing sequence of ordinal functions has regular length which is larger than κ+, then by the Trichotomy Theorem the sequence satisfies one of three structural conditions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length κ+. It is shown that this is not the case.

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The PCF Trichotomy Theorem does not hold for short sequences

Abstract

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