Abstract
Suppose that κ = cf(κ), λ > cf(λ) = κ+ and λ = λκ. We prove that there exist a sequence hBi : i < κi of Boolean algebras and an ultrafilter D over κ so that λ = Q Depth+(Bi)/D < Depth+(Q Bi/D) = λ+. An i<κ i<κ identical result holds also for Length+. The proof is carried in ZFC, and it holds even above large cardinals.
| Original language | English |
|---|---|
| Pages (from-to) | 953-963 |
| Number of pages | 11 |
| Journal | Houston Journal of Mathematics |
| Volume | 45 |
| Issue number | 4 |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019 University of Houston
Keywords
- Boolean algebras
- Depth
- Ultraproducts