Timeline for Turing degree of a turing machine with access to an (arbitrary) nonstandard integer
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 18, 2017 at 19:52 | answer | added | Sam Sanders | timeline score: 1 | |
| Jul 18, 2017 at 17:30 | answer | added | Noah Schweber | timeline score: 4 | |
| Jul 18, 2017 at 10:20 | comment | added | Joel David Hamkins | I've realized a way to make sense of your idea of computing a function with nonstandard help, and in this case, we can determine which are the functions that are computable with nonstandard help. | |
| Jul 18, 2017 at 10:19 | answer | added | Joel David Hamkins | timeline score: 4 | |
| Jul 18, 2017 at 6:41 | review | Close votes | |||
| Jul 18, 2017 at 13:19 | |||||
| Jul 18, 2017 at 6:37 | history | edited | Christopher King | CC BY-SA 3.0 |
deleted 684 characters in body; added 102 characters in body
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| Jul 18, 2017 at 6:36 | history | undeleted | Christopher King | ||
| Jul 17, 2017 at 17:53 | history | deleted | Christopher King | via Vote | |
| Jul 17, 2017 at 17:49 | comment | added | Christopher King | @JoelDavidHamkins sorry, I think I formulated this question really badly. I'm doing to delete it and try again when I get more sleep. | |
| Jul 17, 2017 at 17:33 | comment | added | Joel David Hamkins | I'm sorry, but I just don't know what you mean by giving a Turing machine a nonstandard number as input. There are a variety of different incompatible things that I can imagine you might mean; but without further explanation, it doesn't make sense by itself. | |
| Jul 17, 2017 at 17:24 | comment | added | Christopher King | @JoelDavidHamkins you don't get to pick which one. It's arbitrary (in particular, it must give the same result for every nonstandard integer you supply it). | |
| Jul 17, 2017 at 17:14 | review | Close votes | |||
| Jul 17, 2017 at 18:00 | |||||
| Jul 17, 2017 at 15:15 | comment | added | Joel David Hamkins | If you intend to run a standard Turing machine program inside a nonstandard model of arithmetic or set theory, then basically any set can become computable. Indeed, there is a single (standard) program that can in principle compute any set, if run in the right universe. See jdh.hamkins.org/?s=universal+algorithm&submit=Search. | |
| Jul 17, 2017 at 15:02 | comment | added | Joel David Hamkins | I don't understand the question. What does it mean to give a Turing machine a nonstandard number? | |
| Jul 17, 2017 at 15:01 | comment | added | 喻 良 | It may halt before H but not halt in a standard number. | |
| Jul 17, 2017 at 14:33 | history | asked | Christopher King | CC BY-SA 3.0 |