Finite quasivarieties and self-referential conditions (Q1770617)

The author considers classes of finite (universal) algebras defined by a system of quasi-identities, calling them `finite quasivarieties' or even `farieties'. He introduces a new type of formula, called `recursive quasi-identities', which are implications of the form \(\bigwedge_{1\leq i\leq n}\mathbf e_i\to\mathbf e\) where \(\mathbf e\) is a term equation and the \(\mathbf e_i\) are either term equations or so-called `positive recursive conditions'. The latter allow to express a certain degree of self-reference with the goal of simulating recursive definitions. The main result of the paper is that a class of finite algebras is a fariety if it can be defined by a system of recursive quasi-identities.