Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A NOTE ON WEAK EXCLUDED MIDDLE LAW

  • Chanyoung Sung (Department of Mathematics Education Korea National University of Education)
  • Received : 2023.01.04
  • Accepted : 2023.01.27
  • Published : 2023.02.28
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Abstract

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 ¬𝜑∨¬¬𝜑 for any formula 𝜑. 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.

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References

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