Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Co-theory of sorted profinite groups for PAC structures   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 the "Weak Independence Theorem" for PAC substructures of an ambient
structure with nfcp and the property B(3). Fourth, we describe Kim-dividing in
these PAC substructures and show several results related to the SOPn hierarchy.
Fifth, we characterize the algebraic closure in PAC structures

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom