π-character and depth in scattered Boolean spaces

Wide Scattered Spaces and Morasses

We show that it is relatively consistent with ZFC that 2ω is arbitrarily large and every sequence s = 〈sα : α < ω2〉 of infinite cardinals with sα ≤ 2ω is the cardinal sequence of some locally compact scattered space.

Scattered Spaces 3

On Depth and Depth+ of Boolean Algebras

We show that the Depth of an ultraproduct of Boolean Algebras cannot jump over the Depth of every component by more than one cardinal. Consequently we have similar results for the Depth invariant.

Boolean Metric Spaces and Boolean Algebraic Varieties

The concepts of Boolean metric space and convex combination are used to characterize polynomial maps An −→ Am in a class of commutative Von Neumann regular rings including p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e. sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to t...

Depth of Boolean Algebras

Suppose D is an ultrafilter on κ and λ = λ. We prove that if Bi is a Boolean algebra for every i < κ and λ bounds the Depth of every Bi, then the Depth of the ultraproduct of the Bi’s mod D is bounded by λ. We also show that for singular cardinals with small cofinality, there is no gap at all. This gives a partial answer to problem No. 12 in [?]. 2000 Mathematics Subject Classification. Primary...