Journal of Mathematical Logic 5 (02):149-166 (2005)

We lift Jensen's coding method into the context of Woodin cardinals. By a theorem of Woodin, any real which preserves a "strong witness" to Woodinness is set-generic. We show however that there are class-generic reals which are not set-generic but preserve Woodinness, using "weak witnesses".
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DOI 10.1142/S0219061305000420
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References found in this work BETA

Square in Core Models.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.
Inner Models in the Region of a Woodin Limit of Woodin Cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
Square In Core Models, By, Pages 305 -- 314.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.
The Core Model Iterability Problem.J. R. Steei - 2001 - Studia Logica 67 (1):124-127.

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