HOD dichotomy: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "The HOD dichotomy theorem is a theorem which shows that HOD, the class of hereditarily ordinal-definable sets, must either be close to or far from the true universe, \(V\). It is formulated in analogy with Jensen's original dichotomy theorem, which asserts that one of the two following holds: * Every uncountable cardinal is inaccessible in \(L\). * For every singular \(\gamma\), \(\gamma\) is singular in \(L\) and \((\gamma^+)^L = \gamma^+\)....") |
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The HOD dichotomy theorem is a theorem which shows that [[Ordinal definable|HOD]], the class of hereditarily ordinal-definable sets, must either be close to or far from the true universe, \(V\). It is formulated in analogy with Jensen's original dichotomy theorem, which asserts that one of the two following holds:
* Every uncountable cardinal is inaccessible in [[Constructible hierarchy|\(L\)]].
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