# Variety-infinity-extensible automorphism

## Contents

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This article defines a property that can be evaluated for an automorphism of an algebra in a variety of algebras. The evaluation of that property depends on the ambient variety, and not just on the automorphism or the algebra.
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## Definition

Let $\mathcal{V}$ be a variety of algebras, and $A$ be an algebra in $\mathcal{V}$. An automorphism $\sigma$ of $A$ is termed infinity-extensible over the variety $\mathcal{V}$ if it is $\alpha$-extensible over $\mathcal{V}$ for every ordinal $\alpha$.