turkmath.org

The Axiom of Choice is one of the axioms of ZFC set theory which is equivalent to the well-ordering theorem, the statement which ensures that every set can be well-ordered. The well-ordering theorem seems to trigger an apparatus that we often use in establishing the isomorphism of two objects. In this semi-philosophical talk, we discuss how mathematical entities and known theorems are affected in a state of affairs where the Axiom of Choice is not invoked. Consequently, one gets what we may call "raw" objects that are neither ante-structures, i.e., structures in the most generalized form, nor particular exemplifications of ante-structures.