Almost disjoint abelian groups |
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| Authors: | P. C. Eklof A. H. Mekler S. Shelah |
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| Affiliation: | (1) Institute for Advanced Studies, The Hebrew University of Jerusalem, Jerusalem, Israel;(2) Present address: Department of Mathematics, University of California, 92717 Irvine, CA, USA;(3) Present address: Department of Mathematics, Simon Fraser University, V5A 1S6 Burnaby, British Columbia, Canada;(4) Present address: Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel |
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| Abstract: | Under various set-theoretic hypotheses we construct families of maximal possible size of almost free abelian groups which are pairwise almost disjoint, i.e. there is no non-free subgroup embeddable in two of them. We show that quotient-equivalent groups cannot be almost disjoint, but we show how to construct maximal size families of quotient-equivalent groups of cardinality ℵ1, which are mutually non-embeddable. Dedicated to the memory of Abraham Robinson on the tenth anniversary of this death First and third authors acknowledge assistance from the US-Israel Binational Science Foundation, Grant No. 1110. First author partially supported by NSF Grant No. MCS-8003691. Second author acknowledges support from the National Science and Engineering Research Council of Canada, Grant No. U0075 |
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