Recursive Unary Algebras and Trees

Khoussainov, B. Recursive “nary algebras and trees, Annals of Pure and Applied Logic 67 (1994) 213-268. A unary algebra is an algebraic system d = (A,f,, ,L). wheref,, . ,fm are unary operations on A and n EW. In the paper we develop the theory ofeffective “nary algebras. We investigate well-known questions of constructive (recursive) model theory with respect to the class of unary algebras. In the paper we construct “nary algebras with a finite number of recursive isomorphism types. We give the notions of program, uniform, and algebraic dimensions of models, and then we investigate these notions on unary algebras. We find connections between algebraic and effective properties of r.e. representable unary algebras. We also deal with finitely generated r.e. (positive) unary algebras. We show the connections between trees and “nary algebras. Our interests also concern recursive automorphisms groups, r.e. subalgebra and congruence lattices of effective “nary algebras.