I. Juhász, L. Soukup, Z. Szentmiklóssy:
What is left of CH after you add Cohen reals?
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
- Every initially omega_1 compact, countably tight T_3 space is compact.
- Let X be a countably tight compact T_2 space; then
- if S is G_delta-dense in X then every point of X is the
limit newline of a converging omega_1-sequence from S;
- if Ysubset X with sprd(Y)leomega_1 then hght(Y)leomega_1
- X contains no complete binary tree of closed sets of height omega_2.
- If X is a compact T_2 space with small diagonal then
X is metrizable.
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