Book Review: Cardinal algebras

Book Review

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Constructing Boolean Algebras for Cardinal Invariants

We construct Boolean Algebras answering some questions of J. Donald Monk on cardinal invariants. The results are proved in ZFC (rather than giving consistency results). We deal with the existence of superatomic Boolean Algebras with “few automorphisms”, with entangled sequences of linear orders, and with semi-ZFC examples of the non-attainment of the spread (and hL,hd).

Cardinal invariants of ultraproducts of Boolean algebras

We deal with some of problems posed by Monk [Mo 1], [Mo 3] and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate several new cardinal invariants. AMS 1991 Mathematics Subject Classification primary: 03G05, 03E05, secondary: 06E15, 03E35 ∗ The research was partially supported by DFG grant Ko 490/7-1. This is publication number 534 of the second...

More on Cardinal Invariants of Boolean Algebras

We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that irr(B0 × B1) = max{irr(B0), irr(B1)}. We prove consistency of the statement “there is a Boolean algebra B such that irr(B) < s(B ~ B)” and we force a superatomic Boolean algebra B∗ such that s(B∗) = inc(B∗) = κ, irr(B∗) ...

Book Review