Sh:477

• Brendle, J., Judah, H. I., & Shelah, S. (1992). Combinatorial properties of Hechler forcing. Ann. Pure Appl. Logic, 58(3), 185–199. arXiv: math/9211202 DOI: 10.1016/0168-0072(92)90027-W MR: 1191940
• Abstract:
  Using a notion of rank for Hechler forcing we show:

  1) assuming \omega_1^V = \omega_1^L, 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 \omega_1 and those on the right-hand side equal 2^\omega and produces a maximal almost disjoint family of subsets of \omega of size \omega_1;

  3) there is no perfect set of random reals over V in V[r][d], where r is random over V and d Hechler over V[r].

• Version 1993-09-12_10 (18p) published version (15p)

@article{Sh:477,
 author = {Brendle, J{\"o}rg and Judah, Haim I. and Shelah, Saharon},
 title = {{Combinatorial properties of Hechler forcing}},
 journal = {Ann. Pure Appl. Logic},
 fjournal = {Annals of Pure and Applied Logic},
 volume = {58},
 number = {3},
 year = {1992},
 pages = {185--199},
 issn = {0168-0072},
 mrnumber = {1191940},
 mrclass = {03E40 (03E45)},
 doi = {10.1016/0168-0072(92)90027-W},
 note = {\href{https://arxiv.org/abs/math/9211202}{arXiv: math/9211202}},
 arxiv_number = {math/9211202}
}