Is there a good notion of hypercomputation which allows inaccessible-length computations?

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Good day,

I would like to ask, whether a good notion of hypercomputation which allows inaccessible-length computations exists. I am familiar with a notion of supertask, which is a countably many computational steps in a finite time. Then hypertask which is the same but with uncountably many steps(same as a cardinality of a power set of set of all natural numbers). But is there a notion of an inaccessible-length computation?

Thank you for your answers, Have a nice day.