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 \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.

Relation with other properties

Stronger properties

Weaker properties