Strong subgroup chains and the Baer-Specker group

Oren Kolman

Strong subgroup chains and the Baer-Specker group

Oren Kolman

University of Bedfordshire

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Examples are given of non-elementary properties that are preserved under Cfiltrations for various classes C of abelian groups. The Baer-Specker group ℤw is never the union of a chain áAa : a < dñ of proper subgroups such that ℤw/Aa is cotorsionfree. Cotorsionfree groups form an abstract elementary class (AEC). The Kaplansky invariants of ℤw/ℤ(w) are used to determine the AECs (ℤw/ℤ(w)) and (B/A), where B/A is obtained by factoring the Baer- Specker group B of a ZFC extension by the Baer-Specker group A of the ground model, under various hypotheses, yielding information about its stability spectrum.

Original language	English
Title of host publication	Models, modules and abelian groups: In memory of A.L.S. Corner
Publisher	Walter de Gruyter GmbH
Pages	187-198
ISBN (Print)	9783110203035
Publication status	Published - 1 Jan 2008

Keywords

subgroup chains

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title = "Strong subgroup chains and the Baer-Specker group",

abstract = "Examples are given of non-elementary properties that are preserved under Cfiltrations for various classes C of abelian groups. The Baer-Specker group ℤw is never the union of a chain {\'a}Aa : a < d{\~n} of proper subgroups such that ℤw/Aa is cotorsionfree. Cotorsionfree groups form an abstract elementary class (AEC). The Kaplansky invariants of ℤw/ℤ(w) are used to determine the AECs (ℤw/ℤ(w)) and (B/A), where B/A is obtained by factoring the Baer- Specker group B of a ZFC extension by the Baer-Specker group A of the ground model, under various hypotheses, yielding information about its stability spectrum.",

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T1 - Strong subgroup chains and the Baer-Specker group

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N2 - Examples are given of non-elementary properties that are preserved under Cfiltrations for various classes C of abelian groups. The Baer-Specker group ℤw is never the union of a chain áAa : a < dñ of proper subgroups such that ℤw/Aa is cotorsionfree. Cotorsionfree groups form an abstract elementary class (AEC). The Kaplansky invariants of ℤw/ℤ(w) are used to determine the AECs (ℤw/ℤ(w)) and (B/A), where B/A is obtained by factoring the Baer- Specker group B of a ZFC extension by the Baer-Specker group A of the ground model, under various hypotheses, yielding information about its stability spectrum.

AB - Examples are given of non-elementary properties that are preserved under Cfiltrations for various classes C of abelian groups. The Baer-Specker group ℤw is never the union of a chain áAa : a < dñ of proper subgroups such that ℤw/Aa is cotorsionfree. Cotorsionfree groups form an abstract elementary class (AEC). The Kaplansky invariants of ℤw/ℤ(w) are used to determine the AECs (ℤw/ℤ(w)) and (B/A), where B/A is obtained by factoring the Baer- Specker group B of a ZFC extension by the Baer-Specker group A of the ground model, under various hypotheses, yielding information about its stability spectrum.

KW - subgroup chains

M3 - Chapter

SN - 9783110203035

SP - 187

EP - 198

BT - Models, modules and abelian groups: In memory of A.L.S. Corner

PB - Walter de Gruyter GmbH

ER -

Strong subgroup chains and the Baer-Specker group

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