| Résume | This will be the second talk on our solution, with John Baldwin and James Freitag, to the Koponen conjecture, where in the previous talk we’ve already proven that every supersimple theory with quantifier elimination in a finite relational language has finite SU-rank. In this talk, we discuss pseudolinearity and its connections, from the existing literature, to the group configuration theorem. We then apply it to the Koponen conjecture and Koponen's question on one-basedness, completing the argument that every supersimple theory with quantifier elimination in a finite relational language is one-based. Motivated by our application of pseudolinearity, we then begin the main step of our proof of the Koponen conjecture, where we show that every simple theory with quantifier elimination in a finite relational language is supersimple. In doing so, we further demonstrate the influence of the semantic on the syntactic. |
