منابع مشابه
Stationary Reflection in Extender Models
Working in L[E], we examine which large cardinal properties of κ imply that all stationary subsets of cof(<κ) ∩ κ reflect.
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We give an instance when the extender algebra can preserve stationary subsets of ω1. In particular, we show that for any model operator satisfying certain conditions (satisfied by the currently known minimal inner models for large cardinal statements), any Ω-consistent statement about a rank initial segment of the universe can be forced over canonical model containing H(ω2) while preserving sta...
متن کاملBounded Stationary Reflection
We prove that, assuming large cardinals, it is consistent that there are many singular cardinals μ such that every stationary subset of μ+ reflects but there are stationary subsets of μ+ that do not reflect at ordinals of arbitrarily high cofinality. This answers a question raised by Todd Eisworth.
متن کاملSemistationary and stationary reflection
We study the relationship between the semistationary reflection principle and stationary reflection principles. We show that for all regular cardinals λ ≥ ω2 the semistationary reflection principle in the space [λ] implies that every stationary subset of E ω := {α ∈ λ | cf(α) = ω} reflects. We also show that for all cardinals λ ≥ ω3 the semistationary reflection principle in [λ] does not imply ...
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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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2005
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm187-2-4