### A consistency result on weak reflection

by Cummings and Dzamonja and Shelah. [CDSh:571]

Fundamenta Math, 1995

In this paper we study the notion of strong non-reflection, and
its contrapositive weak reflection. We say theta strongly
non-reflects at lambda iff there is a function
F: theta ---> lambda such that for all alpha < theta
with cf(alpha)= lambda there is C club in alpha such that
F restriction C is strictly increasing. We prove that it is
consistent to have a cardinal theta such that strong
non-reflection and weak reflection each hold on an unbounded set of
cardinals less than theta .

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