What is left of CH after you add Cohen reals?
✍ Scribed by I. Juhász; L. Soukup; Z. Szentmiklóssy
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 710 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
✦ Synopsis
The principle CH* concerning elementary submodels is formulated and is shown to be valid in any generic extension obtained by adding any number of Cohen reals to a ground model satisfying CH.
CH* has interesting topological consequences, e.g.: (i) Every initially wl-compact, countably tight 7'3 space is compact.
(ii) Let X be a countably tight compact TX space; then (a) if S is Gs-dense in X then every point of X is the limit of a converging wl-sequence from S; (b) if Y c X with s(Y) < WI then h(Y) 6 WI; (c) X contains no complete binary tree of closed sets of height ~2.
(iii) If X is a compact TZ space with small diagonal then X is metrizable.