Quantifier expressibility in predicate logic

New mathematical concepts are often introduced with some quantifier definitions. If we have a sufficiently large stock of such notions, it can allow to reformulate the new quantifier definitions in a quantifier-free form. This makes the problem of finding basic concepts, which make further quantifiable definition redundant, worth considering. Creating computer programs that automatically introduce such bases is also worth considering. The present paper considers the quantifier expressibility in 4 algebraic systems. This paper provides bases of quantifier expressibility of small depth.