Non-dominating Ultrafilters
نویسندگان
چکیده
We show that if cov(M) = κ, where κ is a regular cardinal such that ∀λ < κ(2 ≤ κ), then for every unbounded directed family H of size κ there is an ultrafilter UH such that the relativized Mathias forcing M(UH) preserves the unboundedness of H. This improves a result of M. Canjar (see [4, Theorem 10]). We discuss two instances of generic ultrafilters for which the relativized Mathias forcing preserves the unboundedness of certain unbounded families of size < c.
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