Fields definable in the free group
Ayala Byron, Rizos Sklinos
TL;DR
This paper proves that the theory of the free group cannot define any infinite field, highlighting limitations in the definability of algebraic structures within free groups.
Contribution
It establishes a fundamental non-definability result for infinite fields in the theory of free groups, advancing understanding of their logical structure.
Findings
No infinite field is definable in the free group theory
The result constrains the algebraic structures interpretable in free groups
Enhances knowledge of the logical complexity of free groups
Abstract
We prove that no infinite field is definable in the theory of the free group
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