Arities and aritizabilities of first-order theories

Abstract

We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. Arities and aritizabilities are semantically characterized. The dynamics for arities of theories is described. Possibilities for arities and aritizabilities of theories are illustrated by a series of natural geometric, combinatorial and model-theoretic examples.