A characterization of Ext(G,ℤ) assuming (V = L)

Saharon Shelah; Lutz Strüngmann

Fundamenta Mathematicae (2007)

  • Volume: 193, Issue: 2, page 141-151
  • ISSN: 0016-2736

Abstract

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We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence ( ν p : p ∈ Π ) of cardinals satisfying ν p ≤ 2 ν (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that ν p equals the p-rank of Ext(G,ℤ) for every prime p and 2 ν is the torsion-free rank of Ext(G,ℤ).

How to cite

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Saharon Shelah, and Lutz Strüngmann. "A characterization of Ext(G,ℤ) assuming (V = L)." Fundamenta Mathematicae 193.2 (2007): 141-151. <http://eudml.org/doc/283260>.

@article{SaharonShelah2007,
abstract = {We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence $(ν_\{p\}: p ∈ Π)$ of cardinals satisfying $ν_\{p\} ≤ 2^\{ν\}$ (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that $ν_\{p\}$ equals the p-rank of Ext(G,ℤ) for every prime p and $2^\{ν\}$ is the torsion-free rank of Ext(G,ℤ).},
author = {Saharon Shelah, Lutz Strüngmann},
journal = {Fundamenta Mathematicae},
keywords = {Whitehead problem; torsion-free Abelian groups},
language = {eng},
number = {2},
pages = {141-151},
title = {A characterization of Ext(G,ℤ) assuming (V = L)},
url = {http://eudml.org/doc/283260},
volume = {193},
year = {2007},
}

TY - JOUR
AU - Saharon Shelah
AU - Lutz Strüngmann
TI - A characterization of Ext(G,ℤ) assuming (V = L)
JO - Fundamenta Mathematicae
PY - 2007
VL - 193
IS - 2
SP - 141
EP - 151
AB - We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence $(ν_{p}: p ∈ Π)$ of cardinals satisfying $ν_{p} ≤ 2^{ν}$ (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that $ν_{p}$ equals the p-rank of Ext(G,ℤ) for every prime p and $2^{ν}$ is the torsion-free rank of Ext(G,ℤ).
LA - eng
KW - Whitehead problem; torsion-free Abelian groups
UR - http://eudml.org/doc/283260
ER -

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