15-399 Constructive Logic
Lecture 13: Arithmetic

In the previous lecture we introduced first-order logic, where quantifiers range over elements of an unknown domain. If we instead talk about natural numbers we obtain arithmetic. In classical logic, the usual axiom system is called Peano arithmetic; in intuitionistic logic we have Heyting arithmetic. The principal difference between the two is the underlying logic, not the formulation of the natural numbers or properties such as induction.

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Frank Pfenning