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ON THE WEAK FORMS OF CHOICE IN TOPOI

김익성
한국수학교육학회|2008.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제15권 제1호|pp. 85-92

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참고문헌

키워드

axiom of choiceimplicit axiom of choiceaxiom of separated choice.
주제분류수학

초록

In topoi, there are various forms of the axiom of choice such as (ES), (AC) and (WO). And also there are various weak forms of the axiom of choice such as (DES), (IAC) and (ASC). First we investigate the relation between (IAC) and (ASC), and then we study the relation between (AC) and (WO). We get equivalent forms of the axiom of choice in a well-pointed topos.

Abstract

In topoi, there are various forms of the axiom of choice such as (ES), (AC) and (WO). And also there are various weak forms of the axiom of choice such as (DES), (IAC) and (ASC). First we investigate the relation between (IAC) and (ASC), and then we study the relation between (AC) and (WO). We get equivalent forms of the axiom of choice in a well-pointed topos.

참고문헌 (8)

  1. M. Barr, "Topos, Triples and Theories" (1985), Springer-Verlag
  2. R. Diaconescu, "Axiom of Choice and Complementation", Proc. Amer. Math. Soc, 51(1), pp.176~178 (1975)
  3. M.M. Ebrahimi, "The category of M-sets", Ital. J. Pure and Appl. Math, (9), pp.123~132 (2001)
  4. R. Goldblatt, "Topoi" (1984), North-Holland
  5. P.T. Johnstone, "Topos Theory" (1977), Academic Press
  6. A. Madanshekaf, "On the Category of M-Set", Far East J. Math. Sci, (2), pp.251~260 (2000)
  7. M.M. Mawanda, "Well-ordering and Choice", J. Pure and Appl. Algebra, 50, pp.171~184 (1988)
  8. A.M. Penk, "Two Form of the Axiom of Choice for an Elementary Topos", J. Symbolic logic, 40(2), pp.192~212 (1975)

관련 논문AI추천

A study on equivalent forms of the axiom of choice in an well-pointed toposIg Sung Kim대한수학회 · 대한수학회논문집2004 · 제19권 제1호TWO FORMS OF THE AXIOM OF CHOICE ANDWELL-ORDERING IN AN ELEMENTARY TOPOSIgSungKim한국수학교육학회 · 이론수학과 교직수학2003 · 제10권 제3호On the Axiom of choice of weak topos ${\Cal Fuz}$김익성대한수학회 · 대한수학회논문집2006 · 제21권 제2호ON SOME PROPERTIES OF TOPOS E(Ω ,A)김익성한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제4호ON THE WEAK NATURAL NUMBER OBJECT OF THE WEAK TOPOS FUZ김익성한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제2호On the injectivity of the weak topos Fuz김익성강원경기수학회 · 한국수학논문집2009 · 제17권 제2호

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