MathDBThe ordered-abelian-group conjecture on trace-defining fields
The ordered-abelian-group conjecture on trace-defining fields
Let be an ordered abelian group. An infinite field means a field with infinitely many elements.
Ordered-abelian-group conjecture. An ordered abelian group cannot trace define an infinite field.
The paper proves the analogous statement for Presburger arithmetic and several related finite-rank structures, but presents the general ordered-abelian-group assertion as a conjecture.
Sources & referencesView supporting material
Primary source
Erik Walsberg, “Notes on trace equivalence”, arXiv:2101.12194 (2022).
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