最終更新日:2022/12/24
The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let A=(0,1)∪(1,2). Then ¬A=(-∞,0)∪(2,∞), ¬¬A=(0,2), ¬¬A→A=(-∞,1)∪(1,∞) ne ℝ.
編集履歴(0)
The law of double negation is not valid intuitionistically. To show this with Heyting algebra semantics, let A=(0,1)∪(1,2). Then ¬A=(-∞,0)∪(2,∞), ¬¬A=(0,2), ¬¬A→A=(-∞,1)∪(1,∞) ne ℝ.