Partition relations for κ-normal ideals on Pκ(λ)
✍ Scribed by Pierre Matet
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 267 KB
- Volume
- 121
- Category
- Article
- ISSN
- 0168-0072
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📜 SIMILAR VOLUMES
We shall prove that for any regular A and strongly normal A-saturated ideal I on "P,~A the Supfunction is one-to-one on some X E I\*, generalizing Solovay's theorem for normal ultrafilters.
We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no (proper, fine, κ-complete) ideal on Pκ (λ) is weakly λ + -saturated.
## Abstract Given a regular infinite cardinal __κ__ and a cardinal __λ__ > __κ__, we study fine ideals __H__ on __P__~__κ__~(__λ__) that satisfy the square brackets partition relation $ H^{+} {\mathop \rightarrow \limits^{\kappa}} [H^{+}]^{2}\_{\mu} $, where __μ__ is a cardinal ≥2. (© 2003 WILEY‐VC