Functorial Equations for Lexicographic Products

by Kuhlmann and Kuhlmann and Shelah. [KKSh:615]
Proc American Math Soc, 2003
We generalize the main result of [KKSh:601] concerning the convex embeddings of a chain Gamma in a lexicographic power Delta^Gamma . For a fixed nonempty chain Delta, we derive necessary and sufficient conditions for the existence of nonempty solutions Gamma to each of the lexicographic functional equations (Delta^Gamma)^{<= 0} simeq Gamma, (Delta^Gamma) simeq Gamma, and (Delta^Gamma)^{<0} simeq Gamma .

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