There is no a priori reason why the aimed for results should be unprovable ala Gödel. However, it turns out it has been proven that it is. Tao says so in the p

There is no a priori reason why the aimed for results should be unprovable ala Gödel. However, it turns out it has been proven that it is. Tao says so in the post: > I will remark that the general question of determining whether one set of equational axioms determines another is undecidable. Even though the general problem is undecidable, individual instances are still potentially solvable.