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math.LO2020
On countable elementary free groups
Olga Kharlampovich, Christopher Natoli
We prove that if a countable group is elementarily equivalent to a non-abelian free group and all of its abelian subgroups are cyclic, then the group is a union of a chain of regul…
math.LO2020
Non--homogeneity in free groups
Olga Kharlampovich, Christopher Natoli
We prove that non-abelian free groups of finite rank at least 3 or of countable rank are not -homogeneous. We answer three open questions from Kharlampovich, Myasnikov, an…