A forcing construction of thin-tall Boolean algebras

• Autorzy: Juan Carlos Martínez
• Języki publikacji: EN

Abstrakty

EN

It was proved by Juhász and Weiss that for every ordinal α with ${0 < α < ω_2}$ there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that $κ^{< κ} = κ$ and α is an ordinal such that $0 < α < κ^{++}$, then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating this forcing through all $α < κ^{++}$, we obtain a notion of forcing that preserves cardinals and such that in the corresponding generic extension there is a superatomic Boolean algebra of height α and width κ for every $α < κ^{++}$. Consistency for specific κ, like $ω_1$, then follows as a corollary.

Kategorie tematyczne

• 54G12: Scattered spaces
• 03E35: Consistency and independence results
• 06E99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 159
• Numer: 2
• Strony: 99-113

Daty

wydano

1999

otrzymano

1996-03-04

poprawiono

1997-11-24

poprawiono

1998-02-02

poprawiono

1998-09-21

Twórcy

autor

Juan Carlos Martínez

• Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

Bibliografia

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