I was reading about logic systems and the following phrase appeared.
any closed expression that is not derivable inside the same system
What is a "closed expression" in this context? What does "closed expression that is not derivable" mean?
A closed expression (or closed formula) refers to a formula that has no free variables . This is also called sentence.
In a logic system, you have a set of axioms, which are sentences, and rules which state how to derive a sentence from this . If a sentence can be derived from the axioms, this means that the axioms entail this sentence. If a sentence is not derivable, it is not entailed by the axioms.