Re:Gödel, Escher, Bach: an in-depth explainer
by red_trumpet on Wednesday September 14, 2022 @05:16AM
(#32834849)
Wikipedia has a list[1] of statements which are not provable in (or rather independent of) ZFC.
IMO the most weird thing is the following, intertwining consistency of ZFC with Diophantine equations[2]:
> One can write down a concrete polynomial p ∈ Z[x1, ..., x9] such that the statement "there are integers m1, ..., m9 with p(m1, ..., m9) = 0" can neither be proven nor disproven in ZFC (assuming ZFC is consistent). [...] the polynomial is constructed so that it has an integer root if and only if ZFC is inconsistent.
IMO the most weird thing is the following, intertwining consistency of ZFC with Diophantine equations[2]:
> One can write down a concrete polynomial p ∈ Z[x1, ..., x9] such that the statement "there are integers m1, ..., m9 with p(m1, ..., m9) = 0" can neither be proven nor disproven in ZFC (assuming ZFC is consistent). [...] the polynomial is constructed so that it has an integer root if and only if ZFC is inconsistent.
[1] https://en.wikipedia.org/wiki/List_of_statements_independent...
[2] https://en.wikipedia.org/wiki/List_of_statements_independent...