Scales, Topological Reflections, and Large Cardinal Issues
نویسنده
چکیده
Reflection theorems in set-theoretic topology typically take the following form: if all “small” subspaces of a suitable kind of space X have a property P, then so does the whole space. Here “small” often means “of cardinality א1” but in Sections 1 and 2 of this paper it will mean “separable”. Usually, but not always, some sort of large cardinal axiom is needed, and the reflection theorem holds in some forcing extension. The following 1977 result of Shelah illustrates all this nicely:
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