We construct Boolean-valued term models and describe their universal properties. The underlying set of these models consists of the terms of the underlying language, while formulae are interpreted in the Lindenbaum-Tarski algebra of open formulae. Subspaces of the Stone space of the Lindenbaum-Tarski algebra of open formulae are shown to be homeomorphic to spaces of enumerated models models equ...

We study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theo...

We introduce the notion of multiendomorphism in a hypergroupoid and the notion of G-semiring. We show that, if (H, ∗) is a commutative semi-hypergroup, these multiendomorphisms form a G-semiring (E,+, ◦,≤), where the operation + is induced by ∗, ◦ is the usual composition of maps ◦ and ≤ is the usual inclusion of maps. Moreover, we show under which conditions the G-semiring (E,+, ◦,≤) is, in fa...

It was recently shown by the authors that deformations of hypergroup convolutions w.r.t. positive semicharacters can be used to explain probabilistic connections between the Gelfand pairs (SL(d, C), SU(d)) and Hermitian matrices. We here study connections between general convolution semigroups on commutative hypergroups and their deformations. We are able to develop a satisfying theory, if the ...

A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Hypergroups generalize in many ways topological groups. In this paper we extend to compact not necessarily commutative hypergroups some basic techniques on multipliers set forth for compact groups in He...

In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete or non-complete 1-hypergroups. Furthermore, classify the 1-hypergroups size 5 and 6 based on partition induced by fundamental relation ?. Many these can be obtained using aforesaid hypergroup construction.