Pseudo-Logical Class; Interpretability of Theories; Expansion of a Theory; Axiomatizability

Abstract

Let ρ, σ be two arities (finite sequences of natural numbers). Let A be a logical class of arity (ρ, σ), i.e., a class of concatenations (R, S) where R is a ρ-ary multirelation and S a σ-ary multirelation. The class of multirelations R for which there exists S such that (R, S) is in A is called an B- logical class relative to A. The class of all R such that (R, S) is in A for any S with the same base is known as an V-logical class relative to A. Both types are known as pseudo-logical classes.