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.

Logic is a particular kind of formal system in which we call validity truth, and invalidity falsehood. Whether you choose to call the valid propositions of a given formal system true is a matter of semantics. So, you could choose to call your axioms true, however to do so would likely cause some confusion, as it could be seen as implying that you are presupposing the formal system of logic in your analysis.
