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On the Axiom of choice of weak topos ${\Cal Fuz}$

김익성
대한수학회 (The Korean Mathematical Society)|2006.04|대한수학회논문집 (Communications of the KMS)|제21권 제2호|pp. 211-217

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참고문헌

주제분류수학

초록

Abstract

Topos is a set-like category. In topos, the axiom ofchoice can be expressed as (AC1), (AC2) and (AC3). Category{Cal Fuz} of fuzzy sets has a similar function to the topos Set and it forms weak topos. But {Cal Fuz} does notsatisfy (AC1), (AC2) and (AC3). So we define (WAC1), (WAC2) and(WAC3)in weak topos {Cal Fuz}. And we show that they are equivalent in{Cal Fuz}.

참고문헌 (4)

  1. "\ref \key 1 \by R. Diaconescu \paper Axiom of choice andcomplementation \jour Proc. Amer. Math. Soc. \vol 51 \yr 1975\pages no. 1", pp.176~
  2. "\ref \key 4 \by A. M. Penk \paper Two form of the axiom of choicefor an elementary topos \jour J. of Symbolic logic. \vol 40\issue 2 \yr 1975 \pages 192--212\endref"
  3. "Categorical analysis of logic operator on fuzzy sets" (1993)
  4. "Categories of fuzzy sets and weak topos" (2002)

관련 논문AI추천

Weak Axiom of Choice on the Category Fuz김익성한국수학교육학회 · 이론수학과 교직수학2006 · 제13권 제4호A study on equivalent forms of the axiom of choice in an well-pointed toposIg Sung Kim대한수학회 · 대한수학회논문집2004 · 제19권 제1호ON THE WEAK FORMS OF CHOICE IN TOPOI김익성한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제1호ON THE WEAK NATURAL NUMBER OBJECT OF THE WEAK TOPOS FUZ김익성한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제2호On the injectivity of the weak topos Fuz김익성강원경기수학회 · 한국수학논문집2009 · 제17권 제2호TWO FORMS OF THE AXIOM OF CHOICE ANDWELL-ORDERING IN AN ELEMENTARY TOPOSIgSungKim한국수학교육학회 · 이론수학과 교직수학2003 · 제10권 제3호

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