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math.LO2026
Building trees in large fields
Elliot Kaplan, Angus Matthews, Erik Walsberg
We show that large rosy fields are bounded, and substantially simplify the proofs that large stable fields are separably closed and that large simple fields are bounded. Our proofs…
math.LO2026
Geometric fields, ranks, and generic derivations
Antongiulio Fornasiero, Elliot Kaplan, Angus Matthews
In this note, we show various minimality results for a geometric theory of fields : is stable if and only if it is strongly minimal, is simple if and only if it has SU-r…