There are no interesting consistent and complete axiom systems (recently discussed here by probabilistic approches).
This depends pretty heavily on what you mean by interesting, since it requires something like being able to model Peano Arithmetic or at least Robinson arithmetic. But first order reals or first order C are "interesting" systems (in the sense that we study them and there are open problems that can be phrased in terms of them) and are consistent and complete.
First order reals [...] are "interesting" systems (in the sense that we study them and there are open problems that can be phrased in terms of them) and are consistent and complete.
I wasn't aware of that. Can you give some link?
New Salt Compounds Challenge the Foundation of Chemistry
The title is overblown (it depends on what you think the foundation is), but get a load of this:
And here's the philosophical bit:
The obvious example of local truth is relativistic effects being pretty much invisible over the durations and distances that are normal for people, but there's also that the surface of the earth is near enough to flat for many human purposes.
Any suggestions for other truths which could turn out to be local?