Finding bases of uncountable free Abelian groups is usually difficult

Noam Greenberg, Dan Turetsky, Linda Brown Westrick

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4483-4508
Number of pages26
JournalTransactions of the American Mathematical Society
Issue number6
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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