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
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