Construction of free continuous algebras
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A subset system Z is a function, assiging to each posetX a collectionZX of its subsets. We studyZ-continuous universal algebras, i.e., ordered algebras such that their domains have, and their operations preserve, joins of allZ-sets. A construction of the freeZ-continuous algebras is exhibited for an arbitraryZ. It turn out that only four subset systems have to be considered: the systemZX of (i) all ε-chains inX; (ii) all finite subsets ofX; (iii) all countable subsets ofX and (iv) the void set alone. The free algebras are described concretely for these four cases.
KeywordsDisjoint Union Binary Tree Universal Property Algebra UNIV Extension Property
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