Timeline for Undecidable easy arithmetical statement
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 8, 2017 at 12:38 | answer | added | Dominic van der Zypen | timeline score: 15 | |
| Nov 8, 2017 at 10:41 | vote | accept | Ofra | ||
| Nov 8, 2017 at 0:18 | answer | added | Joseph O'Rourke | timeline score: 15 | |
| Nov 7, 2017 at 23:44 | comment | added | Steven Stadnicki | There are several arithmetic examples at mathoverflow.net/questions/11540/… too. | |
| Nov 7, 2017 at 22:12 | answer | added | Lucas K. | timeline score: 10 | |
| Nov 6, 2017 at 20:38 | comment | added | Robert Frost | @Ofra there's one fairly obvious reasons why the Collatz Conjecture might be undecidable, namely because one possible case of it being false is the existence of some sequence which ascends to infinity. Since it could be impossible to follow it to infinity (as to do so might involve infinitely many calculations) it is possible it's undecidable by certain axioms. | |
| Nov 1, 2017 at 1:01 | comment | added | Gerry Myerson | Some of the questions listed under "Related" on this page might give an answer. | |
| Oct 31, 2017 at 22:00 | review | Close votes | |||
| Nov 1, 2017 at 8:19 | |||||
| Oct 31, 2017 at 21:55 | comment | added | Ofra | @Adreas Blass (1) I'm considering ZF. (2) I think your comment is as subjective as mine :-). (3) What you mentioned is one reason I was thinking about but it is not enough. I was wondering if there is a mathematical reason to believe that the conjecture is undecidable. | |
| Oct 31, 2017 at 21:43 | comment | added | Andreas Blass | In my previous comment, I should also have mentioned (3) a more precise description of "some reasons". If I take that phrase literally, then the failure (until now) of a lot of smart people to prove or refute the Collatz conjecture could qualify as some reason to believe it's undecidable (in ZF). But I suspect that's not what you intended. | |
| Oct 31, 2017 at 21:41 | comment | added | Andreas Blass | The question would be better if you indicated (1) undecidable from what axioms? (e.g., Peano arithmetic, Zermelo-Fraenkel set theory, or what) and (2) a criterion for "easy" that doesn't depend on discerning "the spirit of" a mathematical statement. | |
| Oct 31, 2017 at 21:34 | comment | added | Andreas Blass | In at least one precise sense of "easy", namely quantifier complexity, Gödel's original examples were easier than the Collatz conjecture. | |
| Oct 31, 2017 at 21:29 | comment | added | Ofra | Please, if you down vote do tell the reason, May be I can ameliorate my question :-) thanks. | |
| Oct 31, 2017 at 21:18 | history | asked | Ofra | CC BY-SA 3.0 |