Characterization of Partial Lattices on Countable Boolean Lattice
نویسندگان
چکیده
In this paper new concepts countable join property, countable meet property, P–lattice and Pδ –lattice are introduced. We established that P–lattice and Pδ –lattice are measureable partial lattices and characterized partial lattices of a lattice through countable join and meet properties. We also established some interesting result on the injective property of the lattice measurable functions defined over countable Boolean lattices.
منابع مشابه
DIRECTLY INDECOMPOSABLE RESIDUATED LATTICES
The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. The main theorem states that a residuatedlattice A is directly indecomposable if and only if its Boolean center B(A)is {0, 1}. We also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...
متن کاملRegularity in residuated lattices
In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in re...
متن کاملSemi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices
At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...
متن کاملOn the structure of the Medvedev lattice
We investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite Boolean algebra, or contains an antichain of size 2 א0 , the size of the lattice itself. We also prove that it is consistent that the lattice has chains of size 2 א0 , and in fact that these big chains occur in every in...
متن کاملOrdinal Sums of Projectives in Varieties of Lattices
(A for ‘above’; B for ‘below.’) A lattice satisfying this condition is called finitely separable. It is easy to see that every countable lattice is finitely separable. We used this to show the following surprising result: the ordinal sum of two free lattices is projective if and only if one of them is finitely generated or both are countable. In this note we give a complete characterization of ...
متن کامل