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- W3112585575 abstract "The aim of this paper is to consider questions concerning the possible maximum cardinality of various separable pseudoradial (in short: SP) spaces. The most intriguing question here is if there is, in ZFC, a regular (or just Hausdorff) SP of cardinality greater than $mathfrak c$. While this question is left open, we establish a number of non-trivial results that we list: 1. It is consistent with Martin's Axiom and $mathfrak c =aleph_2$ that there is a countably tight and compact SP of cardinality $2^{mathfrak c}$. 2. If $kappa$ is a measurable cardinal then in the forcing extension obtained by adding $kappa$ many Cohen reals, every countably tight regular SP space has cardinality at most $mathfrak c$. 3. If $kappa>aleph_1$ Cohen reals are added to a model of GCH, then in the extension every pseudocompact SP space with a countable dense set of isolated points has cardinality at most $mathfrak c$. 4. If $mathfrak cleqaleph_2$, then there is a 0-dimensional SP space with a countable dense set of isolated points that has cardinal greater than $mathfrak c$." @default.
- W3112585575 created "2020-12-21" @default.
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- W3112585575 date "2020-12-04" @default.
- W3112585575 modified "2023-10-14" @default.
- W3112585575 title "On the cardinality of separable pseudoradial spaces" @default.
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