A <Heyting algebra> is a bounded <distributive lattice> $L$ in which, for every $a,b\in L$, there is an element $a\Rightarrow b$ satisfying
$$
x\leq(a\Rightarrow b)\quad\Longleftrightarrow\quad x\wedge a\leq b.
$$
Thus $a\Rightarrow b$ is the greatest element whose meet with $a$ lies below $b$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 120 / 1 / a / Solution

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A distributive lattice is a <lattice> in which meet distributes over join and, equivalently, join distributes over meet.

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