In the literature, there have been several methods and definitions for working out whether two theories are “equivalent” or not. In this article, we do something subtler. We provide a means to measure distances between formal theories. We introduce two natural notions for such distances. The first one is that of axiomatic distance, but we argue that it might be of limited interest. The more interesting and widely applicable notion is that of conceptual distance which measures the minimum number of (...) concepts that distinguish two theories. For instance, we use conceptual distance to show that relativistic and classical kinematics are distinguished by one concept only. (shrink)

We show that there exists an atomic polyadic equality algebra of dimension n that is elementary equivalent to a completely representable algebra, but its diagonal free reduct is not completely representable.