An example of a finite set of projectors in $E_3$ is exhibited for which no 0-1 measure exists.

Let $X$ be an Archimedean Riesz space and $𝒫\left(X\right)$ its Boolean algebra of all band projections, and put ${𝒫}_e=\{Pe:P\in 𝒫\left(X\right)\}$ and ${ℬ}_e=\{x\in X:x\wedge (e-x)=0\}$, $e\in X^{+}$. $X$ is said to have Weak Freudenthal Property ($WFP$) provided that for every $e\in X^{+}$ the lattice $lin{𝒫}_e$ is order dense in the principal band $e^{dd}$. This notion is compared with strong and weak forms of Freudenthal spectral theorem in Archimedean Riesz spaces, studied by Veksler and Lavrič, respectively. $WFP$ is equivalent to $X^{+}$-denseness of ${𝒫}_e$ in ${ℬ}_e$ for every $e\in X^{+}$, and every Riesz space with sufficiently many projections...

We investigate an algebraic notion of decidability which allows a uniform investigation of a large class of notions of forcing. Among other things, we show how to build σ-fields of sets connected with Laver and Miller notions of forcing and we show that these σ-fields are closed under the Suslin operation.

We study the minimal prime elements of multiplication lattice module $M$ over a $C$-lattice $L$. Moreover, we topologize the spectrum $\pi \left(M\right)$ of minimal prime elements of $M$ and study several properties of it. The compactness of $\pi \left(M\right)$ is characterized in several ways. Also, we investigate the interplay between the topological properties of $\pi \left(M\right)$ and algebraic properties of $M$.

Trillas ([1]) has defined a relational probability on an intuitionistic algebra and has given its basic properties. The main results of this paper are two. The first one says that a relational probability on a intuitionistic algebra defines a congruence such that the quotient is a Boolean algebra. The second one shows that relational probabilities are, in most cases, extensions of conditional probabilities on Boolean algebras.