Define a "computational cardinal" to be an equivalence class (with respect to recursive isomorphism) of subsets of natural numbers.
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These do not satisfy a bunch of properties that you might want them to satisfy.
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Because I got a little carried away with the analogy btwn the Myhill isomorphism theorem and the Schroeder-Bernstein theorem.
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In many categories, CSB fails. In some, it succeeds. John Goodrick's thesis good reading on some cases of this
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