Post's lattice

In logic and universal algebra, Post's lattice denotes the lattice of all clones on a two-element set {0, 1}, ordered by inclusion. It is named for Emil Post, who published a complete description of the lattice in 1941.^[1] The relative simplicity of Post's lattice is in stark contrast to the lattice of clones on a three-element (or larger) set, which has the cardinality of the continuum, and a complicated inner structure. A modern exposition of Post's result can be found in Lau (2006).^[2]

^ E. L. Post, The two-valued iterative systems of mathematical logic, Annals of Mathematics studies, no. 5, Princeton University Press, Princeton 1941, 122 pp.
^ D. Lau, Function algebras on finite sets: Basic course on many-valued logic and clone theory, Springer, New York, 2006, 668 pp. ISBN 978-3-540-36022-3

[1] E. L. Post, The two-valued iterative systems of mathematical logic, Annals of Mathematics studies, no. 5, Princeton University Press, Princeton 1941, 122 pp.

[2] D. Lau, Function algebras on finite sets: Basic course on many-valued logic and clone theory, Springer, New York, 2006, 668 pp. ISBN 978-3-540-36022-3

[1]

[2]