The p-rank of Ext(G, ℤ) in certain models of ZFC

S. Shelah*, L. Strüngmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We prove that if the existence of a supercompact cardinal is consistent with ZFC, then it is consistent with ZFC that the p-rank of Ext (G, ℤ) is as large as possible for every prime p and for any torsion-free Abelian group G. Moreover, given an uncountable strong limit cardinal μ of countable cofinality and a partition of Π (the set of primes) into two disjoint subsets Π0 and Π1, we show that in some model which is very close to ZFC, there is an almost free Abelian group G of size 2μ = μ+ such that the p-rank of Ext (G, ℤ) equals 2μ = μ+ for every p Π0 and 0 otherwise, that is, for p Π1.

Original languageEnglish
Pages (from-to)200-215
Number of pages16
JournalAlgebra and Logic
Volume46
Issue number3
DOIs
StatePublished - May 2007

Keywords

  • Almost free Abelian group
  • Strong limit cardinal
  • Supercompact cardinal
  • Theory ZFC
  • Torsion-free Abelian group

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