Joins and meets in effect algebras

Autor: Binczak, Grzegorz, Kaleta, Joanna, Zembrzuski, Andrzej
Rok vydání: 2021
Předmět:
Druh dokumentu: Working Paper
Popis: We know that each effect algebra $E$ is isomorphic to $\pi(X)$ for some $E$-test spaces $(X,{\cal T})$.We describe when $\pi(x)\lor \pi(y)$ and $\pi(x)\land\pi(y)$ exists for $x,y\in{\cal E}(X,{\cal T})$. Moreover we give the formula for $\pi(x)\lor\pi(x)$ and $\pi(x)\land\pi(y)$ using only $x,y$ and tests which are elements of ${\cal T}$. We obtain an example of finite, not homogeneous effect algebra $E$ such that sharp elements of $E$ form a lattice, whereas $E$ is not a lattice.
Databáze: arXiv