1.Previous
3.Next

It follows from the definition that 1 <= 0 -> a, corresponding to the intuition that any proposition a is implied by a contradiction 0. Although the negation operation ¬a is not part of the definition, it is definable as a -> 0. The intuitive content of ¬a is the proposition that to assume a would lead to a contradiction. The definition implies that a ? ¬a = 0 (non-contradiction). It can further be shown that a <= ¬¬a, although the converse, ¬¬a <= a, is not true in general, that is, double negation elimination does not hold in general in a Heyting algebra.

1.Previous
3.Next