Axiomatic Set Theory à la Dijkstra and Scholten

Acosta Gempeler, Ernesto | 2017

The algebraic approach by E. W. Dijkstra and C. S. Scholten to formallogic is a proof calculus, where the notion of proof is a sequence of equivalencesproved – mainly – by using substitution of ‘equals for equals’. This paper presentsSet, a first-order logic axiomatization for set theory using the approach of Dijk-stra and Scholten. The approach is novel in that the symbolic manipulation offormulas is shown to be an eective tool for teaching axiomatic set theory tosophomore students in mathematics. This paper contains many examples on howargumentative proofs can be easily expressed inSetand points out howSetcanenrich the learning experience of students. These results are part of a larger ef-fort to formally study and mechanize topics in mathematics and computer sciencewith the algebraic approach of Dijkstra and Scholten.