An Arithmetical-like Theory of Hereditarily Finite Sets | Zendy

Márcia R. Cerioli | Zendy; Vitor Krauss | Zendy; Petrúcio Viana | Zendy

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An 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 , arithmetic function , mathematics , 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.

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