1,003 research outputs found
A general tool for consistency results related to I1
In this paper we provide a general tool to prove the consistency of
with various combinatorial properties at typical at
settings with , that does not need a profound knowledge of
the forcing notions involved. Examples of such properties are the first failure
of GCH, a very good scale and the negation of the approachability property, or
the tree property at and
The singular world of singular cardinals
The article uses two examples to explore the statement that, contrary to the common wisdom, the properties of singular cardinals are actually more intuitive than those of the regular ones
Club-guessing, stationary reflection, and coloring theorems
We obtain strong coloring theorems at successors of singular cardinals from
failures of certain instances of simultaneous reflection of stationary sets.
Along the way, we establish new results in club-guessing and in the general
theory of ideals.Comment: Initial public versio
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