• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.211-217
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• 2006

Topos is a set-like category. In topos, the axiom of choice can be expressed as (AC1), (AC2) and (AC3). Category Fuz of fuzzy sets has a similar function to the topos Set and it forms weak topos. But Fuz does not satisfy (AC1), (AC2) and (AC3). So we define (WAC1), (WAC2) and (WAC3) in weak topos Fuz. And we show that they are equivalent in Fuz.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.249-254
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• 2006

Category Fuz of fuzzy sets has a similar function to the topos Set. But Category Fuz forms a weak topos. We show that supports split weakly(SSW) and with some properties, implicity axiom of choice(IAC) holds in weak topos Fuz. So weak axiom of choice(WAC) holds in weak topos Fuz. Also we show that weak extensionality principle for arrow holds in weak topos Fuz.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.75-87
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• 2020

Category F Rel of fuzzy sets and relations does not form a topos. J. Harding, C. Walker and E. Walker [3] showed that FRel has a tensor product and V. Durov [1] introduced basic definitions related to the notion of vectoid endowed with a tensor product. In this paper, we show that FRel forms a quasi topos. Also we show that there are quasi power objects in FRel. And by the use of the concepts of FRel and quasi topos, we get the logic operators of FRel. Moreover, we show that FRel forms a vectoid.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.693-698
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• 2014

Although the category NFHG of normal fuzzy hypergroups is not a topos, it forms a pseudo topos. Also we show that there are pseudo power objects in NFHG.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.341-346
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• 2010

Category $E({\Omega},A)$ forms a topos. We study on some properties of the topos $E({\Omega},A)$. In particular, we show that $E({\Omega},A)$ is well-pointed.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.137-143
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• 2010

Category Fuz of fuzzy sets has a similar function to the Category Set. But it forms a weak topos. We study a natural number object and a weak natural number object in the weak topos Fuz. Also we study the weak natural number object in $Fuz^C$.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.25-29
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• 1995

The topos constructed in [6] is a set-like category that includes among its axioms an axiom of infinity and an axiom of choice. In its final form a topos is free from any such axioms. Set$\^$G/ is a topos whose object are G-set Ψ$\sub$s/:G${\times}$S\longrightarrowS and morphism f:S \longrightarrowT is an equivariants map. We already known that Set$\^$G/ satisfies the weak form of the axiom of choice but it does not satisfies the axiom of the choice.(omitted)

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.131-139
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• 1996

Topos is a set-like category. For an axiom of choice in a topos, F. W. Lawvere and A. M. Penk introduced another versions of the axiom of choice. Also it is showed that general axiom of choice and Penk's axiom of choice are weaker than Lawvere's axiom of choice. In this paper we study that weak form of axiom of choice, axiom of choice, Penk's axiom of choice and Lawvere's axiom of choice are all equivalent in a well pointed topos.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.29-34
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• 2004

There are various forms of the axiom of choice and also various weak forms of the axiom of choice in a topos. This paper give equivalent forms of the axiom of choice in a well-pointed topos.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.19-26
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• 2000

The purpose of the paper is to show that in the Fraenkel-Mostowski topos, the category of the Boolean algebras has enough injectives.