On measures in cartesian products of Boolean algebras
Roman Sikorski (1951)
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Roman Sikorski (1951)
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A. Kamburelis, M. Kutyłowski (1986)
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Wiesław Głowczyński (2005)
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K. P. Bhaskara Rao, M. Bhaskara Rao (1979)
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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.