Special subsets of cf(μ)μ, Boolean algebras and Maharam measure algebras
✍ Scribed by Saharon Shelah
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 792 KB
- Volume
- 99
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
✦ Synopsis
The original theme of the paper is the existence proof of "there is η = η α : α < λ which is a (λ, J )-sequence for Ī = I i : i < δ , a sequence of ideals". This can be thought of as a generalization to Luzin sets and Sierpinski sets, but for the product i<δ dom(I i ), the existence proofs are related to pcf.
The second theme is when does a Boolean algebra B have a free caliber λ (i.e., if X ⊆ B and |X| = λ, then for some Y ⊆ X with |Y | = λ and Y is independent). We consider it for B being a Maharam measure algebra, or B a (small) product of free Boolean algebras, and κ-cc Boolean algebras. A central case is λ = ( ω ) + , or more generally, λ = µ + for µ strong limit singular of "small" cofinality. A second one is µ = µ <κ < λ < 2 µ ; the main case is λ regular but we also have things to say on the singular case. Lastly, we deal with ultraproducts of Boolean algebras in relation to irr(-) and s(-) etc.