Timeline for What are some interesting applications/corollaries of Kleene's Recursion theorem?
Current License: CC BY-SA 4.0
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| Jan 5, 2023 at 23:44 | comment | added | Davis Yoshida | Ah that makes sense and re-reading your answer it's now clear. Thank you! | |
| Jan 5, 2023 at 22:45 | comment | added | Joel David Hamkins | @DavisYoshida It is exactly the same program in the various models—we can write the program down concretely. What differs is in effect is the length of time available for computation, since in a nonstandard model of PA, one can use all the numbers including nonstandard numbers as stages of the computational process. It is at those nonstandard stages of computation where the new elements are added to the universal sequence. | |
| Jan 5, 2023 at 22:15 | comment | added | Davis Yoshida | Is what's happening here that in the various models, a different (is this meaningful?) Turing machine is being picked out, or is the machine somehow a priori fixed and the models just disagree on its behavior? | |
| Jan 5, 2023 at 15:36 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Jan 5, 2023 at 14:29 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Jan 5, 2023 at 13:54 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |