منابع مشابه
Fragility and indestructibility II
In this paper we continue work from a previous paper on the fragility and indestructibility of the tree property. We present the following: (1) A preservation lemma implicit in Mitchell’s PhD thesis, which generalizes all previous versions of Hamkins’ Key lemma. (2) A new proof of theorems the ‘superdestructibility’ theorems of Hamkins and Shelah. (3) An answer to a question from our previous p...
متن کاملFragility and indestructibility of the tree property
We prove various theorems about the preservation and destruction of the tree property at ω2. Working in a model of Mitchell [9] where the tree property holds at ω2, we prove that ω2 still has the tree property after ccc forcing of size א1 or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. Finally we ...
متن کاملUnprepared Indestructibility
I present a forcing indestructibility theorem for the large cardinal axiom Vopěnka’s Principle. It is notable in that there is no preparatory forcing required to make the axiom indestructible, unlike the case for other indestructibility results. §
متن کاملIndestructibility and stationary reflection
If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ-strategically closed forcing and λ is weakly compact, then we show that A = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets} must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to cons...
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We investigate some possible interactions between an indestructibly supercompact cardinal and a generalization of a property originally due to Levinski [18].
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2015
ISSN: 0168-0072
DOI: 10.1016/j.apal.2015.06.002