Interval basic algebras

Ivan Chajda, Miroslav Kolařík

We show that for any basic algebra $\mathcal A=(A;\oplus,\neg,0)$ and elements $a,b\in A$, there can be introduced operations $\oplus_a,\neg_a$ and $\oplus^b,\neg^b$ such that $([a,1];\oplus_a,\neg_a,a)$ and $([0,b];\oplus^b,\neg^b,0)$ are basic algebras again. It is shown that the interval basic algebras on a given basic algebra $\mathcal A$ satisfy the so-called patchwork condition.