An Arithmetical-like Theory of Hereditarily Finite Sets - Cerioli, Márcia R.; Krauss, Vitor; Viana, Petrucio (Anais do Workshop Brasileiro de Lógica (WBL), 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.