Open AccessAn Arithmetical-like Theory of Hereditarily Finite Sets
Author(s) -
Márcia R. Cerioli,
Vitor Krauss,
Petrúcio Viana
Publication year - 2021
Language(s) - English
Resource type - Conference proceedings
DOI - 10.5753/wbl.2021.15774
Subject(s) - peano axioms , converse , axiom , mathematics , arithmetic function , homomorphism , natural number , second order arithmetic , discrete mathematics , order (exchange) , completeness (order theory) , algebra over a field , pure mathematics , mathematical analysis , geometry , finance , economics
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.