Two Boolean Algebras with Extreme Cellular and Compactness Properties

Abstract

In this paper, we construct two kinds of Boolean algebras with extreme cellular properties and nice embedding properties. The extreme cellular properties are a σ — j -linked but not σ — j + 1-linked and ccc but not σ — 2-linked. The nice embedding properties are that they are ZF-definable subalgebras of both P / F and R (see Preliminaries for notation). It is the author's opinion that R contains much of the “ZF-strength” of P / F .