Topos中选择公理的一个等价刻画

doi:10.6040/j.issn.1671-9352.0.2015.396

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (12): 54-57.doi: 10.6040/j.issn.1671-9352.0.2015.396

Topos中选择公理的一个等价刻画

卢涛¹, 王习娟², 贺伟³

1. 淮北师范大学数学科学学院, 安徽淮北 235000;
2. 南京大学数学系, 江苏南京 210097;
3. 南京师范大学数学科学学院, 江苏南京 210097

收稿日期:2015-08-24 修回日期:2015-11-09 出版日期:2015-12-20 发布日期:2015-12-23
作者简介:卢涛(1974-),男,博士,副教授,研究方向为topos理论,范畴论,locle理论.E-mail:lutao7@live.com
基金资助:
国家自然科学基金资助项目(11171156);安徽省高校自然科学研究重点项目(KJ2015A064)

An equivalent characterization of the choice axiom in a Topos

LU Tao¹, WANG Xi-juan², HE Wei³

1. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China;
2. Department of mathematics, Nanjing University, Nanjing 210097, Jiangsu, China;
3. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, Jiangsu, China

Received:2015-08-24 Revised:2015-11-09 Online:2015-12-20 Published:2015-12-23

摘要/Abstract

摘要： 基于Topos中的偏序对象, 以及相应的完备格对象定义, 证明了选择公理的一个新刻画: 选择公理成立当且仅当连续格对象等价于构造性连续格对象。

关键词: 完备格对象, 偏序对象, Topos, 选择公理

Abstract: We give the new definition of complete lattice object and the equivalent characterization of the choice axiom based on the partially ordered object in a Topos: the choice axiom is equivalent to that L is a continuous lattice object if and only if L is a constructive continuous lattice object.

Key words: Topos, the choice axiom, complete lattice object, partially ordered object

中图分类号:

O189.11

卢涛, 王习娟, 贺伟. Topos中选择公理的一个等价刻画[J]. 山东大学学报（理学版）, 2015, 50(12): 54-57.

LU Tao, WANG Xi-juan, HE Wei. An equivalent characterization of the choice axiom in a Topos[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 54-57.

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Topos中选择公理的一个等价刻画

An equivalent characterization of the choice axiom in a Topos

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