Turing completeness among c.e. sets requires that K can simulate any c.e. set's membership problem, but this presupposes a fixed model of computation whose universality is not logically necessary.

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C.e. sets(as a category of mathematical objects): Short for 'computably enumerable sets'—collections of numbers or objects that a computer could theoretically list out, even if it might take forever to list them all.
Turing completeness(as used in logic and computation theory): A property of a system that means it can solve any computational problem that could theoretically be solved by any other computing machine, given enough time and memory.
logically necessary(Distinguished from metaphysical necessity in Swinburne's argument): That which could not fail to exist or be true; its non-existence or falsehood would be a logical contradiction
model of computation(in computer science and logic): A theoretical system that describes how a computer or mathematical machine could solve problems; different models have different capabilities and rules.

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