The Axiom of Choice in an Elementary Theory of Operations and Sets
A theory (ETHOS) is developed in which the concepts of operation, function, and single-valued relation are distinguished. In ETHOS operations (and functions) and sets are treated on a par; the former are not ‘reduced’ to sets of ordered pairs, as in set theory, but neither do sets vanish altogether, as in category theory. The theory, which is formulated constructively and based on intuitionistic logic, provides a natural framework for investigating the Axiom of Choice.
KeywordsEquivalence Relation Choice Function Function Symbol Category Theory Intuitionistic Logic
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