MercurialBlack (npub17z3…he6e) I just read Theorem 3.9 (Recursion Theorem) on page 8 here: https://math.uchicago.edu/~may/REU2016/REUPapers/Wilson.pdf I'd summarize it as saying that, to get a function from N to a set X recursively, you first consider the set of all 'pseudo-graphs' of this function, which are subsets of N x X that are guaranteed to contain the actual graph. You consider the minimal 'pseudo-graph' (by taking intersection within N x X and then show that it is the correct graph. So the construction requires indexing over a set of subsets of N x X.
I'm not sure how general you want things, but I'd imagine that a similar idea of 'constructing the graph of the desired function / relation' would work
☃️merry chrimist☃️ /
npub1pt6…6mf6
2024-01-26 07:15:37
in reply to nevent1q…r3ss
Author Public Key
npub1pt6l3a97fvywrxdlr7j0q8j2klwntng35c40cuhj2xmsxmz696uqfr6mf6Published at
2024-01-26 07:15:37Event JSON
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"content": "nostr:npub17z3zrlvtcp3fyc94vdqdk7y8ccjc7yay998z7wsvl9f0t7yqmjes3uhe6e I just read Theorem 3.9 (Recursion Theorem) on page 8 here: https://math.uchicago.edu/~may/REU2016/REUPapers/Wilson.pdf I'd summarize it as saying that, to get a function from N to a set X recursively, you first consider the set of all 'pseudo-graphs' of this function, which are subsets of N x X that are guaranteed to contain the actual graph. You consider the minimal 'pseudo-graph' (by taking intersection within N x X and then show that it is the correct graph. So the construction requires indexing over a set of subsets of N x X. \n\nI'm not sure how general you want things, but I'd imagine that a similar idea of 'constructing the graph of the desired function / relation' would work",
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