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The PCF Trichotomy Theorem does not hold for short sequences

The PCF Trichotomy Theorem does not hold for short sequences Arch. Math. Logic (2000) 39: 213–218 c Springer-Verlag 2000 The PCF Trichotomy Theorem does not hold for short sequences 1;2 3 Menachem Kojman , Saharon Shelah Department of Mathematics and Computer Science, Ben Gurion University of the Negev, Beer Sheva, Israel Department of Mathematical Sciences, Carnegie-Mellon University, Pittsburgh, PA, USA (e-mail: kojman@cs.bgu.ac.il) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail: shelah@math.huji.ac.il) Received: 17 January 1998 Abstract. The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite  modulo some ideal I.Ifa < -increasing sequence of ordinal functions has regular length which is larger than  , then by the Trichotomy Theorem the sequence satisfies one of three structural condi- tions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length  . It is shown that this is not the case. 1. Introduction The Trichotomy Theorem [5], II,1.2, specifies three alternatives for the struc- ture of an increasing sequence of ordinal functions modulo an ideal on an infinite cardinal  – provided the sequence has regular length  and  is at ++ least  . The natural context of the Trichotomy Theorem http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

The PCF Trichotomy Theorem does not hold for short sequences

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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s001530050143
Publisher site
See Article on Publisher Site

Abstract

Arch. Math. Logic (2000) 39: 213–218 c Springer-Verlag 2000 The PCF Trichotomy Theorem does not hold for short sequences 1;2 3 Menachem Kojman , Saharon Shelah Department of Mathematics and Computer Science, Ben Gurion University of the Negev, Beer Sheva, Israel Department of Mathematical Sciences, Carnegie-Mellon University, Pittsburgh, PA, USA (e-mail: kojman@cs.bgu.ac.il) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail: shelah@math.huji.ac.il) Received: 17 January 1998 Abstract. The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite  modulo some ideal I.Ifa < -increasing sequence of ordinal functions has regular length which is larger than  , then by the Trichotomy Theorem the sequence satisfies one of three structural condi- tions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length  . It is shown that this is not the case. 1. Introduction The Trichotomy Theorem [5], II,1.2, specifies three alternatives for the struc- ture of an increasing sequence of ordinal functions modulo an ideal on an infinite cardinal  – provided the sequence has regular length  and  is at ++ least  . The natural context of the Trichotomy Theorem

Journal

Archive for Mathematical Logic – Springer Journals

Published: Apr 1, 2000

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