# Sh:477

• Brendle, J., Judah, H. I., & Shelah, S. (1992). Combinatorial properties of Hechler forcing. Ann. Pure Appl. Logic, 58(3), 185–199.
• 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)
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},
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}
}