On ultraproducts of Boolean algebras and irr

On Ultraproducts of Boolean Algebras and Irr Sh703

Special Subsets of Cf(µ) Μ, Boolean Algebras and Maharam Measure Algebras Sh620

The original theme of the paper is the existence proof of “there is η̄ = 〈ηα : α < λ〉 which is a (λ, J)-sequence for Ī = 〈Ii : i < δ〉, a sequence of ideals”. This can be thought of as a generalization to Luzin sets and to Sierpinski sets, but for the product ∏ i<δ Dom(Ii), 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 ...

Maharam measure Algebras

The original theme of the paper is the existence proof of “there is η̄ = 〈ηα : α < λ〉 which is a (λ, J)-sequence for Ī = 〈Ii : i < δ〉, a sequence of ideals. This can be thought of as in a generalization to Luzin sets and Sierpinski sets, but for the product ∏ i<δ dom(Ii), the existence proofs are related to pcf. The second theme is when does a Boolean algebraB has free caliber λ (i.e. if X ⊆ B a...

The Depth of Ultraproducts of Boolean Algebras Sh853

We show that if μ is a compact cardinal then the depth of ultraproducts of less than μ many Boolean Algebras is at most μ plus the ultraproduct of the depths of those Boolean Algebras. I would like to thank Alice Leonhardt for the beautiful typing. This research was supported by the United States-Israel Binational Science Foundation First Typed 03/Nov/14 Latest Revision 05/May/3 Typeset by AMS-...

Densities of Ultraproducts of Boolean Algebras

We answer three problems by J. D. Monk on cardinal invariants of Boolean algebras. Two of these are whether taking the algebraic density πA resp. the topological density dA of a Boolean algebra A commutes with formation of ultraproducts; the third one compares the number of endomorphisms and of ideals of a Boolean algebra. In set theoretic topology, considerable effort has been put into the stu...