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- Xavier Caicedo, Germán Enciso, HAHN-BANACH THEOREM AS A CHOICE PRINCIPLE , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 28 No. 106 (2004)
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Abstract
The subobject classifier of a topos is its "object ot truth values" and its morphisms yield the propositional connectives of its inner logic. Continuing previous work for Kripke models, we study connectives on sheaves over topological spaces. These are determined by certain operations in open sets. Monadic and Heyting connectives form a functionally complete basis in any espacial topos. In particular, a single new connective generates all connectives implicit in Heyting's intuitionistic trivalent logic. We provide a complete axiomatization for the corresponding intermediate modal logic. We consider also connectives invariant under local homeomorphisms, and the global uniform choosings of connectives on distinct topological spaces. Toe main results generaliz.e readily to sheaves over complete Heyting algebras.
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