Meaning of De Morgan algebra | Babel Free

Definitions

A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws.

Examples

“Finally it is shown that the compact elements in the congruence lattice of a De Morgan algebra form⟳ a Boolean sublattice.”

“By a topological de Morgan algebra we shall mean⟳ an abstract algebra (A,#92;land⟳,#92;lor,#92;',l) where (A,#92;land⟳,#92;lor,l) is a de Morgan algebra,”

“If (L,#92;le,#123;⁻#125;) is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then (L#92;langle#92;#33;#92;langleS#92;rangle#92;#33;#92;rangle,#92;le,#123;⁻#125;) constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every r#92;inL#92;langle#92;#33;#92;langleS#92;rangle#92;#33;#92;rangle its negation #92;overline#123;r#125;#92;inL#92;langle#92;#33;#92;langleS#92;rangle#92;#33;#92;rangle is defined by (#92;overline#123;r#125;,s)#61;#92;overline#123;(r,s)#125; for every s#92;inS.”

CEFR level