Source: J. Symbolic Logic
Volume 73, Issue 4
I provide indestructibility results for large
cardinals consistent with V=L, such as weakly compact,
indescribable and strongly
unfoldable cardinals. The Main Theorem shows that any strongly
unfoldable cardinal κ can be made indestructible by
< κ-closed, κ-proper forcing. This class of posets
includes for instance all
< κ-closed posets that are either κ⁺-c.c. or
≤ κ-strategically closed as well as finite
iterations of such posets. Since strongly unfoldable
cardinals strengthen both indescribable and weakly
compact cardinals, the Main Theorem therefore makes these
two large cardinal notions similarly
indestructible. Finally, I apply the Main Theorem to obtain a class
forcing extension preserving all strongly
unfoldable cardinals in which every strongly unfoldable cardinal
κ is indestructible by < κ-closed, κ-proper forcing.
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