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- W4244433750 abstract "Publisher SummaryThis chapter discusses the small P-set in ω*. It is proved that there can be no P-points in the ultrafilter space ω*.The chapter proves a theorem in which there can be no small P-sets in ω*. The term “small” here means the Suslin property or the countable chain condition. It is noted that many such sets exist if the continuum hypothesis is assumed. Indeed, let X be any separable compact space. Then, the Gleason G (X) is separable and under CH it can be embedded into the space ω* as a P-set. In the proof, a different kind of forcing is applied. The chapter introduces the notions connected with proper forcing and quotes the theorems used. An ω-proper forcing P is proper. If the factors of an iteration are both ω-proper and bounding, then so is the resulting P. Several theorems are proved in the chapter such as Frankiewicz, Shelah, Zbierski (FSZ), which proves that there is a model of set theory in which c = ω2 and the remainder space ω* has no P-set with the ccc." @default.
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- W4244433750 date "1994-01-01" @default.
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- W4244433750 title "Chapter 10 Small P-set in ω*" @default.
- W4244433750 doi "https://doi.org/10.1016/s0049-237x(08)70188-5" @default.
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