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๐‘-points in iterated forcing extensions

๐‘-points in iterated forcing extensions

Selective ultrafilters exist in direct iterated ccc extensions whose length has uncountable cofinality, as do <italic>p</italic>-points which are not selective. Nonselective <italic>p</italic>-points also exist e.g. in an iterated Laver or Mathias extension of length <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega 2"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ฯ‰<!-- ฯ‰ --></mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> โ€ฆ