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On possible non-homeomorphic substructures of the real line
2002
Proceedings of the American Mathematical Society
We consider the problem, raised by Kunen and Tall, of whether the real continuum can have non-homeomorphic versions in different submodels of the universe of all sets. This requires large cardinals, and we obtain an exact consistency strength: Theorem 1. The following are equiconsistent: (i) ZF C + ∃κ a Jónsson cardinal ; (ii) ZF C + ∃M a sufficiently elementary submodel of the universe of sets with R M not homeomorphic to R. The reverse direction is a corollary to: We further consider the
doi:10.1090/s0002-9939-02-06385-2
fatcat:qf4jie2dujbizoxe4hklhgg2by