(Universidad de los Andes, 2017) Barriga Turriago, Eliana Lucero; Peterzil, Ya'acov; Onshuus Niño, Alf; 79939996; Berarducci, Alessandro; Goodrick, John Richard; Starchenko, Sergei
This thesis investigates semialgebraically connected semialgebraic groups over a sufficiently saturated real closed field R = R = (R, <, +, 0, ., 1) and is therefore contribution to the study of definable groups o o-minimal structures.
(Universidad de los Andes, 2023-08-01) Pinzón Palacios, Santiago Iván; Hasson, Assaf; Onshuus Niño, Alf; 79939996; Cubides Kovacsics, Pablo; Kowalski, Piotr; Peterzil, Kobi
In this thesis we prove the following restricted version of Zilber's Trichotomy:
Let $K=(K,+,\cdot,v,\Gamma)$ be an algebraically closed valued field and let $(G,\+)$ be a K$-definable group that is either the multiplicative group or contains a finite index subgroup that is $ K$-definably isomorphic to a $K$-definable subgroup of $(K,+)$. Then if $\mathcal G=(G,\+,\ldots)$ is a strongly minimal non locally modular structure definable in $ K$ and expanding $(G,\oplus)$, it interprets an infinite field.
