### Combinatorial properties of Hechler forcing

by Brendle and Judah and Shelah. [BJSh:477]

Annals Pure and Applied Logic, 1992

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 Cichon'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] .

Back to the list of publications