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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