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The Heisenberg group, here denoted $H$, is the group of all $3\times 3$ upperunitriangular matrices with entries in the ring $\mathbb{Z}$ of integers. A.G.Myasnikov posed the question of whether or not the universal theory of $H$, inthe language of $H$, is axiomatized, when the models are restricted to$H$-groups, by the quasi-identities true in $H$ together with the assertionthat the centralizers of noncentral elements be abelian. Based on earlierpublished partial results we here give a complete proof of a slightly strongerresult.

An axiomatization for the universal theory of the Heisenberg group