# 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].

- published version (15p)

Bib entry

@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}, doi = {10.1016/0168-0072(92)90027-W}, mrclass = {03E40 (03E45)}, mrnumber = {1191940}, mrreviewer = {Jakub Jasi\'nski}, doi = {10.1016/0168-0072(92)90027-W}, note = {\href{https://arxiv.org/abs/math/9211202}{arXiv: math/9211202}}, arxiv_number = {math/9211202} }