"From a proof-theoretic perspective, Heyting’s calculus is a restriction of classical logic in which the law of excluded middle and double negation elimination have been removed" (1)
"Intuitionistic logic can be understood as a weakening of classical logic, meaning that it is more conservative in what it allows a reasoner to infer" (1)
How is this compatible with:
"The systems ZF and IZF (ZF but without LEM) are equiconsistent." ?
"From a proof-theoretic perspective, Heyting’s calculus is a restriction of classical logic in which the law of excluded middle and double negation elimination have been removed" (1)
"Intuitionistic logic can be understood as a weakening of classical logic, meaning that it is more conservative in what it allows a reasoner to infer" (1)
How is this compatible with:
"The systems ZF and IZF (ZF but without LEM) are equiconsistent." ?
(1) https://en.wikipedia.org/wiki/Intuitionistic_logic
Seems to be quite subtle (proof theoretic strength and consistency strength)
(2) https://mathoverflow.net/questions/126002/interpretability-a...