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Except for §15, we will only have need to construct direct limits of systems indexed by the natural numbers. Moreover, due to our use of equivalence relations ≡ k to interpret equality in individual worlds, it is not clear how to extend our definition to more general direct systems. The proposed definition in Bowen (1975) fails to account for the presence of ≡ k in some applications below; however, whenever the direct system always satisfies m iζ =m ij °m iζ , that definition works (and will be used in §15).
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