Rudimentary and arithmetical constructive set theory

被引：2

作者：

Aczel, Peter ^{[1
,2
]}

机构：

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[2] Univ Manchester, Sch Comp Sci, Manchester M13 9PL, Lancs, England

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2013年 / 164卷 / 04期

关键词：

Constructive set theory; Rudimentary functions; Arithmetic;

D O I：

10.1016/j.apal.2012.10.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to formulate and study two weak axiom systems for the conceptual framework of constructive set theory (CST). Arithmetical CST is just strong enough to represent the class of von Neumann natural numbers and its arithmetic so as to interpret Heyting Arithmetic. Rudimentary CST is a very weak subsystem that is just strong enough to represent a constructive version of Jensen's rudimentary set theoretic functions and their theory. The paper is a contribution to the study of formal systems for CST that capture significant stages in the development of constructive mathematics in CST. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：396 / 415

页数：20

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