Logic Seminar

Juan Felipe Carmona, Universidad Antonio Nariño

"Flatness and CM-triviality in strongly minimal theories with a predicate"

Hrushovski's construction "ab-initio" is a strongly minimal theory that refutes Zilber's trichotomy conjecture. It's associated pregeometry/matroid has two properties called "Flatness" and "CM-triviality", which forbid the existence of an infinite definable group and the existence of an infinite definable field, respectively. In this talk we'll discuss the meaning of Flatness and CM-triviality in strongly minimal sets and  their meaning in strongly minimal sets with an independent dense subset.