For finitary set functors, free algebras and free completely iterative algebras share the same conservative completion as posets, with omega-chains of approximations in the free algebra solving recursive equations in the iterative one.
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On free completely iterative algebras
For finitary set functors, free algebras and free completely iterative algebras share the same conservative completion as posets, with omega-chains of approximations in the free algebra solving recursive equations in the iterative one.