nLab atomic Boolean algebra


Given an element aa of a Boolean algebra (or other poset) AA, recall that aa is an atom in AA if aa is minimal among non-trivial (non-bottom) elements of AA. That is, given any bAb \in A such that bab \leq a, either b=0b = 0 or b=ab = a.

A Boolean algebra AA is atomic if we have b= Ia ib = \bigvee_I a_i for every bAb \in A, where {a i} I\{a_i\}_I is some set of atoms in AA.


Last revised on November 10, 2023 at 13:44:51. See the history of this page for a list of all contributions to it.