Cellularity of free products of Boolean algebras (or topologies)

Shelah, Saharon

Shelah, Saharon

Fundamenta Mathematicae, Tome 163 (2000), p. 153-208 / Harvested from The Polish Digital Mathematics Library

Résumé

The aim this paper is to present an answer to Problem 1 of Monk [10], [11]. We do this by proving in particular that if μ is a strong limit singular cardinal, $θ = {(2^{c f (μ)})}^{+}$ and $2^{μ} = μ^{+}$ then there are Boolean algebras $𝔹_{1}, 𝔹_{2}$ such that $c (𝔹_{1}) = μ, c (𝔹_{2}) < θ b u t c (𝔹_{1} * 𝔹_{2}) = μ^{+}$ . Further we improve this result, deal with the method and the necessity of the assumptions. In particular we prove that if $𝔹$ is a ccc Boolean algebra and $μ^{ℶ_{ω}} \leq λ = c f (λ) \leq 2^{μ}$ then $𝔹$ satisfies the λ-Knaster condition (using the “revised GCH theorem”).

Publié le : 2000-01-01

Zbl 0967.54003

EUDML-ID : urn:eudml:doc:212474

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     author = {Saharon Shelah},
     title = {Cellularity of free products of Boolean algebras (or topologies)},
     journal = {Fundamenta Mathematicae},
     volume = {163},
     year = {2000},
     pages = {153-208},
     zbl = {0967.54003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv166i1p153bwm}
}

Shelah, Saharon. Cellularity of free products of Boolean algebras (or topologies). Fundamenta Mathematicae, Tome 163 (2000) pp. 153-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv166i1p153bwm/

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