Ranks and approximations for families of cubic theories

Abstract

In this paper, we study the rank characteristics for families of cubic theories, as well as new properties of cubic theories as pseudofiniteness and smooth approximability. It is proved that in the family of cubic theories, any theory is a theory of finite structure or is approximated by theories of finite structures. The property of pseudofiniteness or smoothly approximability allows one to investigate finite objects instead of complex infinite ones, or vice versa, to produce more complex ones from simple structures.

Keywords

• approximation of a theory
• cube
• cubic structure
• cubic theory
• pseudofinite theory
• smoothly approximated structure