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

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

2006-09-22

arxiv.org/abs/math/0609637v1

Mathematics

Logic

Scientific paper

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 P_0 and P_1, 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 P_0 and 0 otherwise, i.e. for p in P_1.

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