Chang’s conjecture and semiproperness of nonreasonable posets

@article{Cox2016ChangsCA,
  title={Chang’s conjecture and semiproperness of nonreasonable posets},
  author={Sean D. Cox},
  journal={Monatshefte f{\"u}r Mathematik},
  year={2016},
  volume={187},
  pages={617-633}
}
Let $$\mathbb {Q}$$Q denote the poset which adds a Cohen real then shoots a club through the complement of $$\big ( [\omega _2]^\omega \big )^V$$([ω2]ω)V with countable conditions. We prove that the version of Strong Chang’s conjecture from Todorčević and Torres-Pérez (MLQ Math Log Q 58(4–5):342–347, 2012) implies semiproperness of $$\mathbb {Q}$$Q, and that semiproperness of $$\mathbb {Q}$$Q—in fact semiproperness of any poset which is sufficiently nonreasonable in the sense of Foreman and… CONTINUE READING
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