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Independence of Boolean algebras and forcing

✍ Scribed by Miloš S. Kurilić

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
274 KB
Volume
124
Category
Article
ISSN
0168-0072

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✦ Synopsis

If Ä ¿ ! is a cardinal, a complete Boolean algebra B is called Ä-dependent if for each sequence b ÿ : ÿ ¡ Ä of elements of B there exists a partition of the unity, P, such that each p ∈ P extends b ÿ or b ÿ , for Ä-many ÿ ∈ Ä. The connection of this property with cardinal functions, distributivity laws, forcing and collapsing of cardinals is considered.

📜 SIMILAR VOLUMES

Unsupported Boolean algebras and forcing
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✍ Miloš S. Kurilić 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 179 KB

## Abstract If __κ__ is an infinite cardinal, a complete Boolean algebra B is called __κ__‐supported if for each sequence 〈__b~β~__ : __β__ < __κ__〉 of elements of B the equality $ \wedge$~__α__<__κ__~ $ \vee$~__β__>__α__~ __b~β~__ = $ \vee$ $ \wedge$~__β__∈__A__~ __b__~__β__~ holds. Combinatorial

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## S(z A y ) z S(A), by (c) * S(z) A S(Y) 2 S(A) e S(x) 2 S(A) and S(y) 2 S(A) e C ( s ) s C ( A ) 'and C ( y ) E C ( A ) , by (c) o x € C ( A ) and Y E C ( A ) . Now every ultrafilter is consistent and closed with respect to C, since if U is an ultrafilter and C ( U ) = X , then C({,uu,, . . ., ,