We prove the characteristic zero case of Zilber's Restricted Trichotomy Conjecture. That is,
we show that if $\mathcal M $ is any non-locally modular strongly minimal structure …

We prove Zilber's Trichotomy Conjecture for strongly minimal expansions of two-
dimensional groups, definable in o-minimal structures: Theorem. Let M be an o-minimal …

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, ie, reducts of the ACF-induced …

STRONGLY MINIMAL REDUCTS OF VALUED FIELDS §1. Introduction. In 1980s, Zilber posed
a conjecture [24] asserting that if a strong Page 1 The Journal of Symbolic Logic Volume 81 …

We prove the higher dimensional case of the o-minimal variant of Zilber's Restricted
Trichotomy Conjecture. More precisely, let $\mathcal R $ be an o-minimal expansion of a …

This is the first of two papers where we prove the Zil'ber trichotomy principle for one-
dimensional structures definable in o-minimal ones. Here we prove: Let N be a definable …

Reducts of algebraic curves Page 1 Reducts of algebraic curves draft of December 2, 2015
Assaf Hasson and Dmitry Sustretov 1 Abstract We show that a non-locally modular reduct of …

Let M be a dense o-minimal structure, N an unstable structure interpretable in M. Then there
exists X, definable in N^ eq, such that X, with the induced N-structure, is linearly ordered and …

In this thesis we study the Restricted Trichotomy Conjectures for algebraically closed and o-
minimal fields. These conjectures predict a classification of all sufficiently complex, that is …

But there have been some key recent developments which bring new ideas and techniques
to the table. One of these is the investigation of abstract notions of independence, leading for …