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The free group does not have the finite cover property

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Abstract

We prove that the first order theory of nonabelian free groups eliminates the ∃∞-quantifier (in eq). Equivalently, since the theory of nonabelian free groups is stable, it does not have the finite cover property.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Stevens Institute of Technology, 1 Castle Point Terrace, Hoboken, NJ, 07030, USA

    Rizos Sklinos

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  1. Rizos Sklinos
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Correspondence to Rizos Sklinos.

Additional information

This work has been conducted while the author was supported by a Golda Meir postdoctoral fellowship at the Hebrew University of Jerusalem.

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Sklinos, R. The free group does not have the finite cover property. Isr. J. Math. 227, 563–595 (2018). https://doi.org/10.1007/s11856-018-1748-3

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  • DOI: https://doi.org/10.1007/s11856-018-1748-3

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