arXiv subjects
Publications and source records attributed to Shimon Garti.
We prove a Theorem about the relationship between the Depth of the ultraproduct of Boolean algebras, divided by an ultrafilter, and the products of the depths of each component. This answers (partly) an open problem of Monk.
We deal here with colorings of the pair (mu^+, mu), when mu is a strong limit and singular cardinal. We show that there exists a coloring c, with no refinement. It follows, that the properties of identities of (mu^+, mu) when mu is singular, differ in an essential way from the case of regular mu .
We show that the Depth^+ of an ultraproduct of Boolean Algebras, can not jump over the Depth^+ of every component by more than one cardinality. We can have, consequently, similar results for the Depth invariant.