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A note on weak excluded middle law
성찬영(Chanyoung Sung) 충청수학회 2023 충청수학회지 Vol.36 No.1
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.