algebra universalis

, Volume 14, Issue 1, pp 140–166 | Cite as

Construction of free continuous algebras

  • Jiří Adámek


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.


Disjoint Union Binary Tree Universal Property Algebra UNIV Extension Property 
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  1. [1]
    J. Adámek,Free algebras and automata realizations in the language of categories. Comment. Math. Univ. Carolinae15 (1974), 589–602.MATHMathSciNetGoogle Scholar
  2. [2]
    B. Banaschwski andE. Nelson,Completion of partially ordered sets as reflections. Computer Science Tech. Rep. 79-CS-6, McMaster University, Hamilton, Ontario, Canada, 1979.Google Scholar
  3. [3]
    G. Jarzembski,Algebry v kategorii zbiorow czesciovo uporiadkovanych. Preprint 1–1978, Mathematical Institute of N. Copernicus University, Torun, Poland, 1978.Google Scholar
  4. [4]
    E. Nelson,Z-continuous algebras. To appear.Google Scholar
  5. [5]
    D. Scott,Continuous lattices. Proceedings, 1971 Dalhouisie Conf. Springer Lecture Note Series, 274, Springer-Verlag (1972), 97–136.Google Scholar
  6. [6]
    E. G. Wagner, J. W. Thatcher andJ. B. Wright,A uniform approach to inductive posets and inductive closure. Lecture Notes in Computer Science 53 (MFCS 77 Proceedings), Springer-Verlag 1977.Google Scholar
  7. [7]
    E. G. Wagner, J. W. Thatcher andJ. B. Wright,Free continuous theories. IBM Research Rep. RC 6906, IBM Research Division, 1979.Google Scholar
  8. [8]
    J. Adámek, E. Nelson, Y. Reiterman, Tree constructions of free continuous algebras. To appear.Google Scholar

Copyright information

© Birkhäuser Verlag 1982

Authors and Affiliations

  • Jiří Adámek
    • 1
  1. 1.Faculty of Electrical EngineeringTechnical University PraguePrahaCzechoslovakia

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