Angus Matthews

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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 $T$ : $T$ is stable if and only if it is strongly minimal, $T$ is simple if and only if it has SU-r…

math.LO2026

Residually Constructible Extensions

Pietro Freni, Angus Matthews

Let $T$ be an o-minimal theory expanding $RCF$ and $T_{convex}$ be the common theory of its models expanded by predicate for a non-trivial $T$ -convex valuation ring…