Finding bases of uncountable free abelian groups is usually difficult

2017/09/07 by Noam Greenberg, Greenberg, Noam, Dan Turetsky +3
Mathematics · #03D60 #03E15 #20A10 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03D60 #msc:03E15 #msc:20A10

paper · pdf · doi:10.48550/arxiv.1709.02326

26 pages

arxiv created 2017/09/07 · arxiv updated 2017/09/08

Abstract

We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally hard, depending on the cardinality. For example, we show, under the assumption V=L, that there is a first-order definable free abelian group with no first-order definable basis.

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