Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T18:36:03.265Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on the Implicational Class Generated by a Class of Structures

Published online by Cambridge University Press:  20 November 2018

G. Grätzer  and
H. Lakser
G. Grätzer
Affiliation:
Untversity of Manitoba, Winnipeg Manitoba
H. Lakser
Affiliation:
Untversity of Manitoba, Winnipeg Manitoba
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We use the notations of [2], particularly for operators on classes of structures; in addition, P*r(K) (respectively, Pr(K)) denotes the class of all reduced products of families of structures in K (those with respect to a proper dual ideal, respectively).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 603 - 605
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Fujiwara, T., On the construction of the least universal Horn class containing a given class, Osaka Math J., (to appear).Google Scholar
2. Grätzer, G., Universal algebra, Van Nostrand, Princeton, N.J., 1968.Google Scholar
3. Grätzer, G. and Lakser, H., The structure of psuedocomplemented distributive lattices. II: Congruence extension and amalgamation, Trans. Amer. Math. Soc. 156 (1971), 343–358.Google Scholar
4. Horn, A., On sentences which are true of direct unions of algebras, J. Symbolic Logic 16 (1951), 14–21.Google Scholar
5. Lakser, H., The structure of pseudocomplemented distributive lattices. I: Subdirect decomposition, Trans. Amer. Math. Soc. 156 (1971), 335–342.Google Scholar
6. Mal’cev, A. I., Several remarks on quasivarieties of algebraic systems, (Russian), Algebra i Logika Sem., no. 3, 5 (1966), 3–9.Google Scholar
7. Shafaat, A., Quasivarieties of pseudocomplemented distributive lattices are varieties, Notices Amer. Math. Soc. 17 (1970), 425.Google Scholar