On the p-rank of Ext_Z(G,Z) in certain models of ZFC

2006/09/22 by Saharon Shelah, Shelah, Saharon, Lutz Strüngmann +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0609637

openalex publication_date 2006/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if the existence of a supercompact cardinal is consistent with ZFC, then it is consistent with ZFC that the p-rank of Ext_Z(G, Z) is as large as possible for every prime p and any torsion-free abelian group G . Moreover, given an uncountable strong limit cardinal mu of countable cofinality and a partition of P (the set of primes) into two disjoint subsets P₀ and P₁, we show that in some model which is very close to ZFC there is an almost-free abelian group G of size 2^mu= mu⁺ such that the p-rank of Ext_Z(G,Z) equals 2^mu= mu⁺ for every p in P₀ and 0 otherwise, i.e. for p in P₁.

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