遗传有限集的类算术理论

Anais do II Workshop Brasileiro de Lógica (WBL 2021) Pub Date : 2021-07-18 DOI:10.5753/WBL.2021.15774

Márcia R. Cerioli, Vitor Krauss, Petrucio Viana

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引用次数: 0

摘要

本文根据介绍(二阶)自然数理论时所采用的常用模式，给出了遗传有限集的(二阶)理论。为此，我们考虑三个基本概念和四个公理，它们类似于通常的皮亚诺公理。由此证明了一个同态定理、它的逆定理、范畴定理和一种(语义)完备性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An Arithmetical-like Theory of Hereditarily Finite Sets

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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Anais do II Workshop Brasileiro de Lógica (WBL 2021)

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