Existentially Closed Exponential Fields. (arXiv:1812.08271v1 [math.LO])

We characterise the existentially closed models of the theory of exponential fields. We find the amalgamation bases and characterise the types over them. We define a notion of independence and show that independent systems of higher dimension can also be amalgamated. Using these results we position the category of existentially closed exponential fields in the stability hierarchy as NSOP$_1$ but TP$_2$. 查看全文>>