Weakly compact cardinal: Difference between revisions
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Created page with "A weakly compact cardinal is a certain kind of large cardinal. They were originally defined via a certain generalization of the compactness theorem for first-order logic to certain infinitary logics. However, this is a relatively convoluted definition, and there are a variety of equivalent definitions. These include, letting \(\kappa\) be the cardinal in question and assuming \(\kappa^{< \kappa} = \kappa\): * \(\kappa\) is 0-Ramsey. * \(\kappa\) is \(\Pi^1_1\)-indes..."
RhubarbJayde (talk | contribs) (Created page with "A weakly compact cardinal is a certain kind of large cardinal. They were originally defined via a certain generalization of the compactness theorem for first-order logic to certain infinitary logics. However, this is a relatively convoluted definition, and there are a variety of equivalent definitions. These include, letting \(\kappa\) be the cardinal in question and assuming \(\kappa^{< \kappa} = \kappa\): * \(\kappa\) is 0-Ramsey. * \(\kappa\) is \(\Pi^1_1\)-indes...") |
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