Are axioms assumed to be true in a formal system? In a logical system, there is assignment of truth values to the sentences in the language, and axioms are assigned the true value.
A logical system is a formal system. 
In a formal system, there is no truth value assignment, but there are still axioms. Does that imply that axioms in a formal system are not assumed to be true?
THanks.

For a formal system to be of much interest, it needs to be consistent -- it needs to have at least one model. In that model, the axioms of the system will be true. It doesn't make much sense to talk about the truth of axioms apart from models.
The formal systems of the most interest -- such as Peano arithmetic and Zermelo-Fraenkel set theory - come with particular "intended" models in which the axioms are true. Indeed, a common way of coming up with axioms is to begin with a model and then try to isolate some of its properties as axioms.
