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- Monadic_Boolean_algebra abstract "In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature 〈·, +, ', 0, 1, ∃〉 of type 〈2,2,1,0,0,1〉,where 〈A, ·, +, ', 0, 1〉 is a Boolean algebra.The monadic/unary operator ∃ denotes the existential quantifier, which satisfies the identities (using the received prefix notation for ∃): ∃0 = 0 ∃x ≥ x ∃(x + y) = ∃x + ∃y ∃x∃y = ∃(x∃y). ∃x is the existential closure of x. Dual to ∃ is the unary operator ∀, the universal quantifier, defined as ∀x := (∃x' )'. A monadic Boolean algebra has a dual definition and notation that take ∀ as primitive and ∃ as defined, so that ∃x := (∀x ' )' . (Compare this with the definition of the dual Boolean algebra.) Hence, with this notation, an algebra A has signature 〈·, +, ', 0, 1, ∀〉, with 〈A, ·, +, ', 0, 1〉 a Boolean algebra, as before. Moreover, ∀ satisfies the following dualized version of the above identities: ∀1 = 1 ∀x ≤ x ∀(xy) = ∀x∀y ∀x + ∀y = ∀(x + ∀y).∀x is the universal closure of x.".
- Monadic_Boolean_algebra wikiPageID "1018197".
- Monadic_Boolean_algebra wikiPageRevisionID "599718542".
- Monadic_Boolean_algebra hasPhotoCollection Monadic_Boolean_algebra.
- Monadic_Boolean_algebra subject Category:Algebraic_logic.
- Monadic_Boolean_algebra subject Category:Boolean_algebra.
- Monadic_Boolean_algebra subject Category:Closure_operators.
- Monadic_Boolean_algebra type Abstraction100002137.
- Monadic_Boolean_algebra type ClosureOperators.
- Monadic_Boolean_algebra type Function113783816.
- Monadic_Boolean_algebra type MathematicalRelation113783581.
- Monadic_Boolean_algebra type Operator113786413.
- Monadic_Boolean_algebra type Relation100031921.
- Monadic_Boolean_algebra comment "In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature 〈·, +, ', 0, 1, ∃〉 of type 〈2,2,1,0,0,1〉,where 〈A, ·, +, ', 0, 1〉 is a Boolean algebra.The monadic/unary operator ∃ denotes the existential quantifier, which satisfies the identities (using the received prefix notation for ∃): ∃0 = 0 ∃x ≥ x ∃(x + y) = ∃x + ∃y ∃x∃y = ∃(x∃y). ∃x is the existential closure of x. Dual to ∃ is the unary operator ∀, the universal quantifier, defined as ∀x := (∃x' )'.".
- Monadic_Boolean_algebra label "Monadic Boolean algebra".
- Monadic_Boolean_algebra label "Monadyczna algebra Boole'a".
- Monadic_Boolean_algebra label "一元布尔代数".
- Monadic_Boolean_algebra sameAs Monadyczna_algebra_Boole'a.
- Monadic_Boolean_algebra sameAs m.03zq6q.
- Monadic_Boolean_algebra sameAs Q6897884.
- Monadic_Boolean_algebra sameAs Q6897884.
- Monadic_Boolean_algebra sameAs Monadic_Boolean_algebra.
- Monadic_Boolean_algebra wasDerivedFrom Monadic_Boolean_algebra?oldid=599718542.
- Monadic_Boolean_algebra isPrimaryTopicOf Monadic_Boolean_algebra.