Corpus ID: 232335642

Local mantles of $L[x]$

  title={Local mantles of \$L[x]\$},
  author={Farmer Schlutzenberg},
Assume ZFC. Let κ be a cardinal. Recall that a < κ-ground is a transitive proper class W modelling ZFC such that V is a generic extension of W via a forcing P ∈ W of cardinality < κ, and the κ-mantle Mκ is the intersection of all < κ-grounds. Assume there is a Woodin cardinal and a proper class of measurables, and let x be a real of sufficiently high Turing degree. Let κ be a limit cardinal of L[x] of uncountable cofinality in L[x]. Using methods from Woodin’s analysis of HOD, we analyze M L[x… Expand


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