ABSTRACT
Recall that for a language L equipped with the 5 standard connectives we defined a collection of sentences in L called tautologies; cf. 5.9. In what follows (essentially throughout the course) we assume that L is a language equipped with the 5 standard connectives ∧,∨,¬,→,↔, quantifiers ∀,∃, and equality = and we assume L has definitions and witnesses. We shall define in what follows two more classes of sentences in L called quantifier axioms and equality axioms, respectively. Using these we shall define theories and proofs.
