Combinatorial Properties of Hechler Forcing

  title={Combinatorial Properties of Hechler Forcing},
  author={J{\"o}rg Brendle and Haim Judah and Saharon Shelah},
  journal={Ann. Pure Appl. Logic},
Using a notion of rank for Hechler forcing we show: 1) assuming ω 1 = ω L 1 , there is no real in V [d] which is eventually different from the reals in L[d], where d is Hechler over V ; 2) adding one Hechler real makes the invariants on the left-hand side of Cichoń’s diagram equal ω1 and those on the right-hand side equal 2 ω and produces a maximal almost disjoint family of subsets of ω of size ω1; 3) there is no perfect set of random reals over V in V [r][d], where r is random over V and d… CONTINUE READING

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