Displaying similar documents to “Congruences and Boolean filters of quasi-modular p-algebras”

Boolean powers as algebras of continuous functions

Bernhard Banaschewski, Evelyn Nelson

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CONTENTSIntroduction................................................. 51. Fundamentals................................................ 72. Functorial aspects......................................... 113. Congruences.................................................. 184. Exponent laws................................................ 285. Finite A............................................................. 346. Boolean ultrapowers..................................... 377. Elementary properties.....................................

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.