TY - JOUR
T1 - The p-rank of Extℤ(G, ℤ) in certain models of ZFC
AU - Shelah, S.
AU - Strüngmann, L.
PY - 2007/5
Y1 - 2007/5
N2 - 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 ℤ(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 ℤ(G, ℤ) equals 2μ = μ+ for every p Π0 and 0 otherwise, that is, for p Π1.
AB - 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 ℤ(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 ℤ(G, ℤ) equals 2μ = μ+ for every p Π0 and 0 otherwise, that is, for p Π1.
KW - Almost free Abelian group
KW - Strong limit cardinal
KW - Supercompact cardinal
KW - Theory ZFC
KW - Torsion-free Abelian group
UR - http://www.scopus.com/inward/record.url?scp=34548227341&partnerID=8YFLogxK
U2 - 10.1007/s10469-007-0019-x
DO - 10.1007/s10469-007-0019-x
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AN - SCOPUS:34548227341
SN - 0002-5232
VL - 46
SP - 200
EP - 215
JO - Algebra and Logic
JF - Algebra and Logic
IS - 3
ER -