Publication date
April 1991
DOI Publisher
Published by Elsevier B.V. ISSN
0166-8641Abstract
AbstractFor every κ let L(κ) denote the quotient Boolean algebra P(κ)[κ]<κ. We would like to answer the well-known question of whether the following consistent statement holds in ZFC: S: (∀κ)(∀λ)[κ≠λ⇒L(κ) is not isomorphic to L(λ)]. It is known that GCH implies S. We find S too hard so we consider the easier question of whether for each n ∈ ω we have:Sn:(∀ κ ≠ ωn)[L(κ) is not isomorphic to L(ωn)]. In this paper we shall prove Sn for all n but one; however, we cannot prove Sn for any specific n. In addition, we also prove that if every Boolean algebra of size at most ω2 embeds into L(ω1), then CH
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