An Arithmetical-like Theory of Hereditarily Finite Sets
Márcia R. Cerioli, Vitor Krauss, Petrúcio Viana · 2021
This paper presents the (second-order) theory of hereditarily finite sets according to the usual pattern adopted in the presentation of the (second-order) theory of natural numbers. To this purpose, we consider three primitive concepts, together with four axioms, which are analogous to the usual Peano axioms. From them, we prove a homomorphism theorem, its converse, categoricity, and a kind of (semantical) completeness.