Variety-infinity-extensible automorphism

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 $$\alpha$$.

Stronger properties

 * Weaker than::I-automorphism
 * Weaker than::Variety-infinity-pushforwardable automorphism

Weaker properties

 * Stronger than::Variety-chain-extensible automorphism
 * Stronger than::Variety-extensible automorphism