Timeline for Is there a nonstandard model of arithmetic having precisely one inductive truth predicate?
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| Oct 23, 2020 at 13:20 | history | edited | YCor |
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| Nov 11, 2014 at 23:22 | vote | accept | Joel David Hamkins | ||
| Nov 11, 2014 at 19:10 | comment | added | Joel David Hamkins | Yes, I agree. Any two truth predicates, in any context with induction able to consider them both, must agree. So different inductive truth predicates cannot satisfy induction in the joint language with both of them. | |
| Nov 11, 2014 at 18:55 | comment | added | Ali Enayat | In light of the nature of the proof given in my answer to the question, it is amusing to note that the existence of more than one inductive full satisfaction predicate on the same countable model of PA provides an interesting example of the fact that the union of two inductive expansions of the same model of PA need not be inductive. Of course one can also produce such examples with forcing, but here the expanisons are somehow more tangible, hence making the failure of induction more dramatic. | |
| Nov 11, 2014 at 16:47 | answer | added | Ali Enayat | timeline score: 15 | |
| Nov 11, 2014 at 14:34 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Nov 11, 2014 at 14:13 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Nov 11, 2014 at 14:05 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Nov 11, 2014 at 13:35 | history | asked | Joel David Hamkins | CC BY-SA 3.0 |