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Journal of the Chungcheong Mathematical Society Volume 36, No. 1.jpg
KCI등재 학술저널

A note on weak excluded middle law

Intuitionistic Zermelo-Fraenkel (IZF) set theory is a set theory without the axiom of choice and the law of excluded middle (LEM). The weak excluded middle law (WEM) states that $\neg\varphi \vee \neg\neg\varphi$ for any formula $\varphi$. In IZF we show that LEM is equivalent to WEM plus the condition that any set not equal to the empty set has an element.

1. Introduction

2. Proof of Theorem 1.1

3. Discussion

References

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