If we have a set of sentences S in first order logic. We know that we can create a first order theory Th(S) from S, which is the "set S" union "the sentences which we can prove them from S" . Also as first order theory, this theory follow the rules (axioms and rules of inferences) of first order logic. Does it has sense to define the Th(S) as above but with an extra union with "axioms of first order logic" ? Also can i consider the Th(S) as formal system which has "intersection" with the formal system First Order Logic?
2026-03-25 12:49:44.1774442984
Connection of axioms of first order logic and axioms of first order theory
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