Similarities and proximity of complete theories (Q1174054)

In Section 1 we give, from a certain general position, characteristics of syntactic and semantic similarities of theories and of definability of one theory in another and give an example of semantically similar, but syntactically dissimilar, theories. Section 2 is of preparatory nature for Section 3. In it, we define the notion of a neutral type and describe such types in theories of polygons. In Section 3 we propose a construction which enables us to construct for an arbitrary algebraic system \(\mathfrak A\) a polygon \({\mathfrak A}_ n\) such that \(\text{Th}({\mathfrak A}_ n)\) is a hull or an almost hull of \(\text{Th}({\mathfrak A})\).