JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (12): 54-57.doi: 10.6040/j.issn.1671-9352.0.2015.396

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An equivalent characterization of the choice axiom in a Topos

LU Tao1, WANG Xi-juan2, HE Wei3   

  1. 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

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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

CLC Number: 

  • O189.11
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[1] LU Tao, WANG Xi-juan, HE Wei. The supremum and infimum of partially ordered objects in a topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 112-117.
[2] LU Tao, WANG Xi-juan, HE Wei. The operator theory on complete partially ordered objects in a topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 64-71.
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