Timeline for What logic characterizes relative intrinsic complexity in set recursion?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| S Mar 20, 2021 at 21:04 | history | bounty ended | CommunityBot | ||
| S Mar 20, 2021 at 21:04 | history | notice removed | CommunityBot | ||
| Mar 16, 2021 at 19:38 | comment | added | Noah Schweber | @SamSanders I guess I still don't see how that can be used here. | |
| Mar 16, 2021 at 18:26 | comment | added | Sam Sanders | I should have been more specific: if something does not work in S1-S9-recursion theory, then it is (often) because of the reasons I mentioned (no T-predicate and the recursion thm is given via S9, which is one monolithic inductive definition), | |
| Mar 15, 2021 at 21:04 | comment | added | Noah Schweber | @SamSanders I'm not sure I quite get what you mean. In E-recursion, the recursion theorem is proved as in classical recursion theory - I think this is analogous to one of Kleene's alternate presentations of his schemes (I know there are a bunch of equivalent formulations kicking around)? But the reverse-math complexity doesn't seem relevant here, as far as I can tell. Incidentally, one could separately ask about an AKMSC theorem for higher type functionals as well; this is something I've also been thinking about recently. | |
| Mar 15, 2021 at 21:01 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Mar 15, 2021 at 18:27 | comment | added | Sam Sanders | So I do not know the answer, but can offer some perspective: in the case of Kleene's S1-S9, there is no "Kleene T predicate" and the recursion theorem is essentially postulated via S9, as S1-S8 only give one primitive recursion (in higher types). Both imply that one cannot talk about S1-S9 computability in weak systems (say higher-order ATR_0 is needed). Is something similar going on with E-recursion? | |
| Mar 12, 2021 at 23:25 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| S Mar 12, 2021 at 19:33 | history | bounty started | Noah Schweber | ||
| S Mar 12, 2021 at 19:33 | history | notice added | Noah Schweber | Draw attention | |
| Dec 30, 2020 at 21:44 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Dec 30, 2020 at 20:08 | history | asked | Noah Schweber | CC BY-SA 4.0 |