[drdeca]

I doubt it. Physics doesn’t seem to have much which is clearly connected to proof systems.

And, besides, from any (consistent) axiom system for which a given statement is undecidable, there is another axiom system which is the same except it adds that statement as an additional axiom, and the statement is therefore (trivially) provable in that system.

And, it doesn’t seem like physics is constrained to use only some specific axiom system.

It seems to me that the relevant thing to physics would be, rather than an axiom system, instead, a model (in the math sense, not the physics sense).

[mirimir]

Thanks.

But doesn't that lead to systems with infinite numbers of axioms?

[drdeca]

If you want to add axioms in order to be able to show each of an infinite number of statements which are all independent of the initial axiom system, and also none of them follow from the rest of them, that could involve an infinite set of axioms, yes,

but any statement we could make about stuff in physics, if it could be expressed in the language of the formal system, would, as a single statement, be something that could be added as a single axiom.