A consistency result on weak reflection

@inproceedings{Cummings1995ACR,
  title={A consistency result on weak reflection},
  author={James Cummings},
  year={1995}
}
In this paper we study the notion of strong non-reflection, and its contrapositive weak reflection. We say θ strongly non-reflects at λ iff there is a function F : θ −→ λ such that for all α < θ with cf(α) = λ there is C club in α such that F 1 C is strictly increasing. We prove that it is consistent to have a cardinal θ such that strong non-reflection and weak reflection each hold on an unbounded set of cardinals less than θ. 1 

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