Timeline for Tuple machinery in I-Sigma_0
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Sep 17, 2010 at 1:57 | vote | accept | CommunityBot | ||
| Sep 16, 2010 at 4:09 | comment | added | user5810 | Don't worry Dave, I will accept your answer, I'm just hoping Joel will respond first. | |
| Sep 15, 2010 at 22:25 | comment | added | Dave Marker | I've edited my answer to include references. | |
| Sep 15, 2010 at 22:25 | history | edited | Dave Marker | CC BY-SA 2.5 |
added 445 characters in body
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| Sep 15, 2010 at 22:08 | comment | added | user5810 | Excellent point, Joel. Although, if I-Sigma_0 doesn't prove "For all n, there is a number coding the set of numbers less than n", this would seem to contradict the statement that it "is able to perform basic Goedel coding" from your answer to my other question. Also, is there an online reference for McAloon's result? | |
| Sep 15, 2010 at 21:01 | comment | added | Joel David Hamkins | Ricky, you don't need that the initial segment is computable---if you know the whole structure is computable, then the fact that there is a nonstandard iniinitial segment with PA gives you a nonstandard $d$ with a code for the halting problem for computations of length $d$, and then you simply appeal to the arithmetic of the big structure again, to find the computable separation as I explained in my answer to the other question. | |
| Sep 15, 2010 at 19:19 | comment | added | user5810 | Does he then prove that there is a decidable such initial segment? In either case, do you have a reference? | |
| Sep 15, 2010 at 18:31 | history | answered | Dave Marker | CC BY-SA 2.5 |