Author:
JALILI SOMAYE,POURMAHDIAN MASSOUD,TAVANA NAZANIN ROSHANDEL
Abstract
Abstract
As a continuation of ideas initiated in [19], we study bi-colored (generic) expansions of geometric theories in the style of the Fraïssé–Hrushovski construction method. Here we examine that the properties
$NTP_{2}$
, strongness,
$NSOP_{1}$
, and simplicity can be transferred to the expansions. As a consequence, while the corresponding bi-colored expansion of a red non-principal ultraproduct of p-adic fields is
$NTP_{2}$
, the expansion of algebraically closed fields with generic automorphism is a simple theory. Furthermore, these theories are strong with
$\operatorname {\mathrm {bdn}}(\text {"}x=x\text {"})=(\aleph _0)_{-}$
.
Publisher
Cambridge University Press (CUP)