Diego’s Theorem for nuclear implicative semilattices

Varieties of Implicative Semilattices

A Jump Inversion Theorem for the Semilattices of Sigma-degrees

We prove an analogue of the jump inversion theorem for the semilattices of Σ-degrees of structures. As a corollary, we get similar result for the semilattices of degrees of presentability of countable structures.

Strong quota pair systems and May's theorem on median semilattices

STRONG QUOTA PAIR SYSTEMS AND MAY’S THEOREM ON MEDIAN SEMILATTICES Lucas Hoots May 12, 2015 Kenneth May [16], in 1952, characterized simple majority rule in terms of three conditions: anonymity, neutrality, and positive responsiveness. In this thesis, we remove the condition of neutrality and obtain a characterization of the class of voting rules that satisfy anonymity and positive responsivene...

Positive Implicative Ordered Filters of Implicative Semigroups

We introduce the notion of positive implicative ordered filters in implicative semigroups. We show that every positive implicative ordered filter is both an ordered filter and an implicative ordered filter. We give examples that an ordered filter (an implicative ordered filter) may not be a positive implicative ordered filter. We also give equivalent conditions of positive implicative ordered f...

Fuzzy Positive Implicative Ordered Filters of Implicative Semigroups

We consider the fuzzification of the notion of a positive implicative ordered filter in implicative semigroups. We show that every fuzzy positive implicative ordered filter is both a fuzzy ordered filter and a fuzzy implicative ordered filter. We give examples that a fuzzy (implicative) ordered filter may not be a fuzzy positive implicative ordered filter. We also state equivalent conditions of...