Define a "computational cardinal" to be an equivalence class (with respect to recursive isomorphism) of subsets of natural numbers.
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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Myhill shows CSB when objects 2-colorings of N, and morphisms computable maps N→N preserving such colorings
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More straightforward cat where objects subsets of N and morphisms computable maps only required to behave well
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make that using the language of "smaller" and "larger" for cardinals based on existence of injections is often not well
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thought out for issues it gets applied to.
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[Ok, yeah, Twitter is terrible. If ever I feel like talking math again, and you're up for hearing it, I will use DM]
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Boy, I particularly screwed this up when dropping a name from the replies for more chars. Well, you can prolly piece together
End of conversation
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