Corpus ID: 228743803

The Virtual Large Cardinal Hierarchy

  title={The Virtual Large Cardinal Hierarchy},
  author={Stamatis Dimopoulos and Victoria Gitman and Dan Saattrup Nielsen},
We continue the study of the virtual large cardinal hierarchy, initiated in [5], by analysing virtual versions of superstrong, Woodin, Vopěnka, and Berkeley cardinals. Gitman and Schindler showed that virtualizations of strong and supercompact cardinals yield the same large cardinal notion [5]. We show the same result for a (weak) virtualization of Woodin and a virtualization of Vopěnka cardinals. We also show that there is a virtually Berkeley cardinal if and only if the virtual Vopěnka… Expand

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