Submission date: 23 May 2019

Abstract:

We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove a &$+#147;weak independence theorem” for PAC substructures of an ambient structure with nfcp and property B(3). Fourth, we describe Kim-dividing in these PAC substructures and show several results related to NSOP. Fifth, we characterize the algebraic closure in PAC structures.

Mathematics Subject Classification: 03C95, 03C45, 03C52

Keywords and phrases: pseudo-algebraically closed structures, Galois groups, Kim-independence

Full text arXiv 1905.09748: pdf, ps.