Computational cardinals are partially ordered: [A] ≤ [B] iff A is one-one reducible to B.
Define a "computational cardinal" to be an equivalence class (with respect to recursive isomorphism) of subsets of natural numbers.
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Thanks. Twitter will use this to make your timeline better. UndoUndo
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Operations defined on computational cardinals:
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[A]+[B] = [{2n | n∈A} ∪ {2n+1 | n∈B}].
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reminds me a little bit of Cantor's integer pairing function: https://en.wikipedia.org/wiki/Pairing_function#Cantor_pairing_function … but with fewer desirable properties
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It's usually called the join of A and B. See https://en.wikipedia.org/wiki/Turing_degree#Turing_equivalence …
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Hi Are there any solving book for exercises in universal algebra?
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We weren't discussing universal algebra above, but https://math.berkeley.edu/~gbergman/245/3.3.pdf … contains universal algebra exercises.
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Thanks!
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I've often said thinking in terms of "computational cardinals" provides a clearer perspective for many issues regarding the
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transfinite, about which people standardly parrot things which seem to me in some ways misguided.
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(Altho, I realize again Twitter not best context for carrying out lengthy math discussions, so I'll leave it at that for now)
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