arXiv subjects
Publications and source records attributed to Mohamed Habibi.
We compare two existence principles for maximal ideals, a classical one for vector lattices with a strong unit and a second, newly introduced one for vector lattices with a strong truncation. Although the latter strictly generalizes the former, we show that the two statements are equivalent over ZF set theory.
In this work we investigate the transfer of fundamental order and completeness properties between truncated Riesz spaces and their unitizations. Specifically, we provide characterizations and equivalences for several notions of completeness: the Archimedean property, relatively uniform completeness, Dedekind completeness, lateral completeness, universal completeness, and the projection property. Counterexamples are presented to illustrate the necessity of assumptions and the independence of various completeness notions.