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math.LO2023
Interpretations of syntactic fragments of theories of fields
Sylvy Anscombe, Arno Fehm
We set up general machinery to study interpretations of fragments of theories. We then apply this to existential fragments of theories of fields, and especially of henselian valued…
math.NT2023
A survey of local-global methods for Hilbert's Tenth Problem
Sylvy Anscombe, Valentijn Karemaker, Zeynep Kisakürek +3
Hilbert's Tenth Problem (H10) for a ring R asks for an algorithm to decide correctly, for each , whether the diophantine equation $f(X_{1},...,X_…
math.LO2023★ 4 cited
Ax-Kochen-Ershov principles for finitely ramified henselian fields
Sylvy Anscombe, Philip Dittmann, Franziska Jahnke
We study the model theory of finitely ramified henselian valued fields of fixed initial ramification, obtaining versions of the Ax-Kochen-Ershov principle as follows. We identify t…