In Chap. 10 we got acquainted with mathematical structures such as groups, rings, integral domains, fields, and Boolean algebras. As discussed there, the benefit of abstracting the common properties of various systems into a unifying structure is that, once we prove certain statements about a structure using only the properties that apply to all models of the structure, they will then be true for each system that models the structure. In this chapter we see examples for such axiomatic proofs.
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