Maximal Dedekind completion of a half lattice ordered group
We study free sequences and related notions on Boolean algebras. A free sequence on a BA is a sequence of elements of , with an ordinal, such that for all with we have . A free sequence of length exists iff the Stone space has a free sequence of length in the topological sense. A free sequence is maximal iff it cannot be extended at the end to a longer free sequence. The main notions studied here are the spectrum function and the associated min-max function Among the results...
In set theory without the axiom of choice (AC), we observe new relations of the following statements with weak choice principles.
In this paper we define maximal MV-algebras, a concept similar to the maximal rings and maximal distributive lattices. We prove that any maximal MV-algebra is semilocal, then we characterize a maximal MV-algebra as finite direct product of local maximal MV-algebras.
Coherent ideals, strongly coherent ideals, and -closed ideals are introduced in pseudo-complemented distributive lattices and their characterization theorems are derived. A set of equivalent conditions is derived for every ideal of a pseudo-complemented distributive lattice to become a coherent ideal. The notion of median prime ideals is introduced and some equivalent conditions are derived for every maximal ideal of a pseudo-complemented distributive lattice to become a median prime ideal which...