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math.LO2024
Strongly Minimal Relics of T-convex Fields
Benjamin Castle, Assaf Hasson
Generalizing previous work on algebraically closed valued fields (ACVF) and o-minimal fields, we study strongly minimal relics of real closed valued fields (RCVF), and more general…
math.LO2024
The O-minimal Zilber Conjecture in Higher Dimensions
Benjamin Castle
We prove the higher dimensional case of the o-minimal variant of Zilber's Restricted Trichotomy Conjecture. More precisely, let be an o-minimal expansion of a real clo…
math.LO2024
Zilber's Trichotomy in Hausdorff Geometric Structures
Benjamin Castle, Assaf Hasson, Jinhe Ye
We give a new axiomatic treatment of the Zilber trichotomy, and use it to complete the proof of the trichotomy for relics of algebraically closed fields, i.e., reducts of the ACF-i…