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- W2913482893 abstract "Abstract Todorcevic introduced the forcing axiom PFA(S) and established many consequences. We contribute to this project. In particular, we consider status under PFA(S) of two important consequences of PFA concerning spaces of countable tightness. We prove that the existence of a Souslin tree does not imply the existence of a compact non-sequential space of countable tightness. We contrast this with M.E. Rudin's result that the existence of a Souslin tree does imply the existence of an S-space (and the later improvement by Dahrough to a compact S-space). On the other hand, PFA(S) implies there is a first-countable perfect pre-image of ω 1 that contains no copies of ω 1 ." @default.
- W2913482893 created "2019-02-21" @default.
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- W2913482893 date "2019-04-01" @default.
- W2913482893 modified "2023-09-29" @default.
- W2913482893 title "PFA(S) and countable tightness" @default.
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- W2913482893 doi "https://doi.org/10.1016/j.topol.2019.01.021" @default.
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