Boolean algebras


Boolean algebras are a mathematical structure which shares the algebraic properties of propositional formulas. Canonical examples include propositional formulas and the power set of a set (with set union, intersection, and complement playing the roles of the propositional connectives). Boolean algebras are used in topology, model theory, and social choice theory.


This concept has the prerequisites:


  • Define a lattice
  • Define a Boolean algebra (as a complemented distributed lattice)
  • Be able to prove simple facts about Boolean algebras
  • Show that the power set of a set, with the standard set operations, forms a Boolean algebra
  • Give an example of a Boolean algebra which is not a power set
  • Define an atom
  • Be aware of the principle of duality (that Boolean algebras are symmetric with respect to meet and join)

Core resources (read/watch one of the following)


Notes on Logic (2013)
Lecture notes for a course on first order logic.
Author: Henry Cohn


See also

-No Additional Notes-