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The study of algebraic structures and properties applying to large classes of such structures. For example, ideas from group theory and ring theory are extended and considered for structures with other signatures (systems of basic or fundamental operations).
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Primitive recursive arithmetic via universal algebra
From the Wikipedia article on Primitive recursive arithmetic:
"Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem[1] …