- Tytuł:
- Cellularity of free products of Boolean algebras (or topologies)
- Autorzy:
- Shelah, Saharon
- Powiązania:
- https://bibliotekanauki.pl/articles/1205001.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
set theory
pcf
Boolean algebras
cellularity
product
colourings - Opis:
-
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, $θ = (2^{cf(μ)})^+$ and $2^μ = μ^+$ then there are Boolean algebras $\mathbb{B}_1,\mathbb{B}_2$ such that
$c(\mathbb{B}_1) = μ, c(\mathbb{B}_2) < θ but c(\mathbb{B}_1*\mathbb{B}_2)=μ^+$.
Further we improve this result, deal with the method and the necessity of the assumptions. In particular we prove that if $\mathbb{B}$ is a ccc Boolean algebra and $μ^{ℶ_ω} ≤ λ = cf(λ) ≤ 2^μ$ then $\mathbb{B}$ satisfies the λ-Knaster condition (using the "revised GCH theorem"). - Źródło:
-
Fundamenta Mathematicae; 2000, 166, 1-2; 153-208
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł