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Published online by Cambridge University Press: 20 February 2018
An additive basis $A$ is finitely stable when the order of
$A$ is equal to the order of
$A\cup F$ for all finite subsets
$F\subseteq \mathbb{N}$. We give a sufficient condition for an additive basis to be finitely stable. In particular, we prove that
$\mathbb{N}^{2}$ is finitely stable.