جستجوی مقالات مرتبط با کلیدواژه "mv algebras" در نشریات گروه "ریاضی"

In this survey we consider the variety of unsharp orthomodular lattices. We will see that there are pretty smooth conditions that neatly generalize a great deal of the theory of orthomodular lattices. In particular, we will characterize the concept of block in this framework towards an appropriate notion of commutativity. Then, we capitalize on this fact and describe a categorical equivalence between orthomodular lattices, with fixed p-filters, and the variety of unsharp orthomodular lattices.

Some results about set theory and model theory of MV-algebras are collected, which allows us to count MV-algebras with various properties.

‎In this paper we consider MV-algebras and their prime spectrum‎. ‎We show that there is an uncountable MV-algebra that has the same spectrum as the free MV-algebra over one element‎, ‎that is‎, ‎the MV-algebra $Free_1$ of McNaughton functions from $[0,1]$ to $[0,1]$‎, ‎the continuous‎, ‎piecewise linear functions with integer coefficients‎. ‎The construction is heavily based on Mundici equivalence between MV-algebras and lattice ordered abelian groups with the strong unit‎. ‎Also‎, ‎we heavily use the fact that two MV-algebras have the same spectrum if and only if their lattice of principal ideals is isomorphic‎.‎As an intermediate step we consider the MV-algebra $A_1$ of continuous‎, ‎piecewise linear functions with rational coefficients‎. ‎It is known that $A_1$ contains $Free_1$‎, ‎and that $A_1$ and $Free_1$ are equispectral‎. ‎However‎, ‎$A_1$ is in some sense easy to work with than $Free_1$‎. Now‎, ‎$A_1$ is still countable‎. ‎To build an equispectral uncountable MV-algebra $A_2$‎, ‎we consider certain ``almost rational'' functions on $[0,1]$‎, ‎which are rational in every initial segment of $[0,1]$‎, ‎but which can have an irrational limit in $1$‎.‎We exploit heavily‎, ‎via Mundici equivalence‎, ‎the properties of divisible lattice ordered abelian groups‎, ‎which have an additional structure of vector spaces over the rational field‎.