# Variety-infinity-extensible automorphism

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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 be a variety of algebras, and be an algebra in . An automorphism of is termed **infinity-extensible** over the variety if it is -extensible over for every ordinal .