A topological set theory implied by ZF and GPK+∞

Por • 29 sep, 2013 • Sección: Opinion

Andreas Fackler

Abstract: We present a system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On  the one hand, this system is acommon weakening of Zermelo-Franenkel set theory ZF, the positive set theory GPK and he theory of hyperuniverses. On the other hand, it retains most of the expressiveness of theses theories and has the same consistency strength as ZF. We single out the additional axiom of the universal set as the one that increases the consistency strength to that of GPK and explore several other axioms and interrlations between those theories. Our results are independent of whether the empty class is a set and whether atoms exist.


Journal of Logic & Analysis 5:1 (2013)


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