Quantifier Free Definability on Infinite Algebras
Bakh Khoussainov · 2016
An operation f: An → A on the domain A of an algebra A is definable if there exists a first order logic formula Φ(x, y) with parameters from A such that for all ā ∈ An and b ∈ A we have f (ā) = b iff A ⊨ Φ (ā, b). The goal of this paper is to study definability of operations by quantifier-free formulas on countable infinite algebras from computability and model-theoretic definability points of view.