Timeline for Finite Number of Registers and Computable Well-Orderings
Current License: CC BY-SA 3.0
11 events
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| Aug 26, 2017 at 12:47 | comment | added | SSequence | Good work with the edit. So, assuming this to be correct (which I assume it quite likely is), this would settle the question2(A). I will be perusing it slowly. So this leaves question1(question in first part) and question2(B), both of which relate to isomorphism. | |
| Aug 26, 2017 at 9:24 | history | edited | Deedlit | CC BY-SA 3.0 |
removed faulty proof of question 1
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| Aug 26, 2017 at 8:39 | history | edited | Deedlit | CC BY-SA 3.0 |
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| Aug 26, 2017 at 8:34 | history | edited | Deedlit | CC BY-SA 3.0 |
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| Aug 25, 2017 at 7:18 | comment | added | SSequence | Small note: I used the phrases "representation of $Value_1$" and "representation of successor function" interchangeably "representation function of $Value_1$" and "representation function of successor function" respectively to make it a little easier to read. It is already clear that we have only one well-ordering relation that is under consideration (so there is no ambiguity in that regard). | |
| Aug 25, 2017 at 6:56 | comment | added | SSequence | The first part of question remains unresolved (in terms of reasoning of why it should be true, if it is). That's because if a given register value (say the function is $Value_1$) is allowed to repeat (which does happen in case of two registers), then it isn't possible (even for $\omega$) in general to extract the representation of successor function from the representation of function $Value_1$ alone. | |
| Aug 24, 2017 at 14:14 | comment | added | SSequence | I think if one can prove that the lower bounds you provided for question2(A) are also upper bounds, then that would resolve that particular part of question. | |
| Aug 24, 2017 at 14:10 | comment | added | SSequence | I am not certain about the reasoning related to first part of question. For the second, I think one would expect lower bounds similar to what you have described (so I suppose it is most likely correct). Though just pointing one particular point in question2(A): One also has to make sure the representation functions (corresponding to register values) will be recursive in some recursive well-ordering (for the ordinals of form $\varphi(n-1,0)$ that you are describing). Though certainly that would be the case for system of register values you described. | |
| Aug 23, 2017 at 23:05 | history | edited | Deedlit | CC BY-SA 3.0 |
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| Aug 23, 2017 at 20:44 | history | edited | Deedlit | CC BY-SA 3.0 |
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| Aug 23, 2017 at 19:21 | history | answered | Deedlit | CC BY-SA 3.0 |