Define a "computational cardinal" to be an equivalence class (with respect to recursive isomorphism) of subsets of natural numbers.
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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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[A]·[B] = [{(n,m) | n∈A, m∈B}], where (,) is a recursive bijection ℕ^2 → ℕ.
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complement([A]) = [ℕ∖A].
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These do not satisfy a bunch of properties that you might want them to satisfy.
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then why?
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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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