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 interpreted in an algebraically closed field $K$ of characteristic zero, then $\mathcal M$ itself interprets $K$; in particular, any non-1-based structure interpreted in $K$ is mutually interpretable with $K$. Notably, we treat both the `one-dimensional' and `higher-dimensional' cases of the conjecture, introducing new tools to resolve the higher-dimensional case and then using the same tools to recover the previously known one-dimensional case.Comment: 75 page
Over algebraically closed fields of arbitrary characteristic, we prove a general multiplicity-freene...
We investigate the isomorphism types of combinatorial geometries arising from Hrushovski's at strong...
We investigate the question of whether the existence of a family of local zero-cycles of degree $d$ ...
In this thesis we study the Restricted Trichotomy Conjectures for algebraically closed and o-minimal...
Abstract. Let N be a structure definable in an o-minimal structureM and p ∈ SN (N), a complete N-1-t...
An infinite structure $M $ is minimal if every definable subset (using param-eters in $M$) is finite...
We characterize those functions f: C → C definable in o-minimal expansions of the reals for which th...
In [5] E. Hrushovski proved the following theorem: Theorem 0.1 (Hrushovski’s New Strongly Minimal Se...
A b s t r a c t. We investigate minimal first-order structures and consider interpretability and def...
AbstractWe formulate an analogue of Zilber's conjecture for o-minimal structures in general, and the...
This thesis explores the geometric principles underlying many of the known Trichotomy Theorems. The ...
This thesis explores the geometric principles underlying many of the known Trichotomy Theorems. The ...
We introduce a new notion of tame geometry for structures admitting an abstract notion of balls. The...
Locally o-minimal structures are some local adaptation from o-minimal structures. They were investig...
In this paper we provide new examples of geometrically trivial strongly minimal differential algebra...
Over algebraically closed fields of arbitrary characteristic, we prove a general multiplicity-freene...
We investigate the isomorphism types of combinatorial geometries arising from Hrushovski's at strong...
We investigate the question of whether the existence of a family of local zero-cycles of degree $d$ ...
In this thesis we study the Restricted Trichotomy Conjectures for algebraically closed and o-minimal...
Abstract. Let N be a structure definable in an o-minimal structureM and p ∈ SN (N), a complete N-1-t...
An infinite structure $M $ is minimal if every definable subset (using param-eters in $M$) is finite...
We characterize those functions f: C → C definable in o-minimal expansions of the reals for which th...
In [5] E. Hrushovski proved the following theorem: Theorem 0.1 (Hrushovski’s New Strongly Minimal Se...
A b s t r a c t. We investigate minimal first-order structures and consider interpretability and def...
AbstractWe formulate an analogue of Zilber's conjecture for o-minimal structures in general, and the...
This thesis explores the geometric principles underlying many of the known Trichotomy Theorems. The ...
This thesis explores the geometric principles underlying many of the known Trichotomy Theorems. The ...
We introduce a new notion of tame geometry for structures admitting an abstract notion of balls. The...
Locally o-minimal structures are some local adaptation from o-minimal structures. They were investig...
In this paper we provide new examples of geometrically trivial strongly minimal differential algebra...
Over algebraically closed fields of arbitrary characteristic, we prove a general multiplicity-freene...
We investigate the isomorphism types of combinatorial geometries arising from Hrushovski's at strong...
We investigate the question of whether the existence of a family of local zero-cycles of degree $d$ ...