The Algebraic Specifications do not have the Tennenbaum Property

Abstract

It is commonly believed that a programmable model satisfying the axioms of a given algebraic specification guarantees good properties and is a correct implementation of the specification. This convinction might be related to the Tennenbaum's property[Ten] of the arithmetic: every computable model of the Peano arithmetic of natural numbers is isomorphic to the standard model. Here, on the example of stacks, we show a model satisfying all axioms of the algebraic specification of stacks which can not be accepted as a good model in spite of the fact that it is defined by a program. For it enables to ”pop” a stack infinitely many times.