Titel
HOD IN INNER MODELS WITH WOODIN CARDINALS
Autor*in
GRIGOR SARGSYAN
DEPARTMENT OF MATHEMATICS, RUTGERS UNIVERSITY
Abstract
We analyze the hereditarily ordinal definable sets HOD in Mn(x)[g] for a Turing cone of reals x, where Mn(x) is the canonical inner model with n Woodin cardinals build over x and g is generic over Mn(x) for the Lévy collapse up to its bottom inaccessible cardinal. We prove that assuming Π1n+2 -determinacy, for a Turing cone of reals x, HODMn(x)[g]=Mn(M∞|κ∞,Λ), where M∞ is a direct limit of iterates of Mn+1 , δ∞ is the least Woodin cardinal in M∞ , κ∞ is the least inaccessible cardinal in M∞ above δ∞ , and Λ is a partial iteration strategy for M∞ . It will also be shown that under the same hypothesis HODMn(x)[g] satisfies GCH .
Stichwort
HODdeterminacyinner model theorylarge cardinalWoodin cardinalmouse
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
The Journal of Symbolic Logic
Band
86
Ausgabe
3
ISSN
0022-4812
Erscheinungsdatum
2021
Seitenanfang
871
Seitenende
896
Publication
Cambridge University Press (CUP)
Erscheinungsdatum
2021
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s), 2021
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