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For our purposes here, there is no need to distinguish between constant symbols and “variables” (“free generators”), since all isomorphism types of abolutely free algebras occur without them.
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Mycielski, J., Taylor, W. A compactification of the algebra of terms. Algebra Universalis 6, 159–163 (1976). https://doi.org/10.1007/BF02485827
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DOI: https://doi.org/10.1007/BF02485827