Metric Boolean algebras and constructive measure theory

Constructive Metric Completion of Boolean Algebras

Filter theory in MTL-algebras based on Uni-soft property

‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

Dynamic equivalence relation on the fuzzy measure algebras

The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

Boolean Algebras and Distributive Lattices Treated Constructively

Some aspects of the theory of Boolean algebras and distributive lattices -in particular, the Stone Representation Theorems and the properties of filters and ideals -are analyzed in a constructive setting.

Equational Varieties of Boolean Functions via the Hsp Theorem

A variant of a theorem of Ekin, Foldes, Hammer and Hellerstein concerning equational characterizations of Boolean function classes is proved using methods of universal algebra. The proof is not constructive but establishes a direct connection with the Birkhoff-Tarski HSP Theorem and the theory of equational classes of universal algebras.