Continuous Algebras Revisited

✍ Scribed by J. Adamek; E. Nelson; J. Reiterman

• Book ID: 102970596
• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 845 KB
• Volume: 51
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1006/jcss.1995.1082

✦ Synopsis

For finitary (Z)-continuous algebras (where (Z) is a subset system), the Birkhoff Variety Theorem is proved in a new way, by means of the logic of inequalities. For infinitary separately (\Delta)-continuous algebras, a counterexample is presented (i.e., an HSP-class which is not a variety). In the logic of jointly (Z)-continuous algebras, tautologies are proved to be independent of (Z), which provides a simple argument for the existence of absolutely free jointly (Z)-continuous algebras. C 1995 Academic Press, Inc.