A Loomis-Sikorski theorem for logics
Jiří Binder (1988)
Mathematica Slovaca
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Jiří Binder (1988)
Mathematica Slovaca
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Paul R. Halmos (1954-1956)
Compositio Mathematica
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Pavel Pták (1985)
Mathematica Slovaca
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Roman Sikorski (1963)
Colloquium Mathematicae
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Sylvia Pulmannová (1981)
Mathematica Slovaca
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Bernhard Banaschewski (1993)
Commentationes Mathematicae Universitatis Carolinae
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The functor taking global elements of Boolean algebras in the topos of sheaves on a complete Boolean algebra 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 -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.