Displaying similar documents to “Algebraic logic, I. Monadic boolean algebras”

On Boolean modus ponens.

Sergiu Rudeanu (1998)

Mathware and Soft Computing

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An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].

On the injectivity of Boolean algebras

Bernhard Banaschewski (1993)

Commentationes Mathematicae Universitatis Carolinae

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The functor taking global elements of Boolean algebras in the topos 𝐒𝐡 𝔅 of sheaves on a complete Boolean algebra 𝔅 is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in 𝔅 -valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial injectives, and (ii) the category of frames has no absolute retracts.