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Simple axioms that are obviously true in \(\mathbb{N}\). (English) Zbl 1303.03090

Summary: We discuss simple subtheories of Peano arithmetic over languages which include the monus function. The system \(\mathrm{ZDL}\) corresponds with \(\mathrm{PA}^-\). The choice of language permits our theories to have special universal axiomatizations; their classes of models have corresponding model theoretic properties.

MSC:

03F30 First-order arithmetic and fragments
03C05 Equational classes, universal algebra in model theory
03C62 Models of arithmetic and set theory
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Full Text: Euclid