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arXiv · 2001.09904

Non-$\forall$-homogeneity in free groups

Olga Kharlampovich·Christopher Natoli
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Abstract

We prove that non-abelian free groups of finite rank at least 3 or of countable rank are not $\forall$-homogeneous. We answer three open questions from Kharlampovich, Myasnikov, and Sklinos regarding whether free groups, finitely generated elementary free groups, and non-abelian limit groups form special kinds of Fra\"iss\'e classes in which embeddings must preserve $\forall$-formulas. We also provide interesting examples of countable non-finitely generated elementary free groups.

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BibTeXRIS

Olga Kharlampovich, Christopher Natoli. 2020-01-27. Non-$\forall$-homogeneity in free groups. https://arxiv.org/abs/2001.09904

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