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A consistency result on cardinal sequences of scattered Boolean spaces

✍ Scribed by Juan C. Martínez

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
119 KB
Volume
51
Category
Article
ISSN
0044-3050

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✦ Synopsis

We prove that if GCH holds and τ = κα : α < η is a sequence of infinite cardinals such that κα ≥ |η| for each α < η, then there is a cardinal-preserving partial order that forces the existence of a scattered Boolean space whose cardinal sequence is τ .

📜 SIMILAR VOLUMES

On cardinal sequences of scattered space
On cardinal sequences of scattered spaces
✍ Juan Carlos Martínez 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 741 KB

It was proved by Dow and Simon that there are 2"' (as many as possible) pairwise nonhomeomorphic compact, T2, scattered spaces of height WI and width w. In this paper, we prove that if cy is an ordinal with WI < 01 < w2 and 19 = (KC: [ < cx) is a sequence of cardinals such that either KC = w or KC =