So I just completed the non-compactness, and incompleteness section of the Standford Introduction to logic online course, and I have developed a few questions.
When mentioning compactness, they also mention the notion of finite subsets of sentences. However in the logic they construct, called Herbrand logic (HL), there is no way to specify a finite subset of a Herbrand base, in the deductive system itself.
How to we define the notion of finite subset of sentences in HL?
Since they do not define what a finite subset of sentences in HL is, they must be reasoning in a meta system about HL.…
When mentioning compactness, they also mention the notion of finite subsets of sentences. However in the logic they construct, called Herbrand logic (HL), there is no way to specify a finite subset of a Herbrand base, in the deductive system itself.
How to we define the notion of finite subset of sentences in HL?
Since they do not define what a finite subset of sentences in HL is, they must be reasoning in a meta system about HL.…