Fantastic filters of lattice implication algebras

Abstract

The notion of a fantastic filter in a lattice implication algebra is introduced, and the relations among filter, positive implicative filter, and fantastic filter are given. We investigate an equivalent condition for a filter to be fantastic, and state an extension property for fantastic filter.

Keywords

• Lattice implication algebra
• filter
• implicative filter
• positive implicative filter
• fantastic filter.