TY - JOUR
T1 - Combinatorial properties of Hechler forcing
AU - Brendle, Jörg
AU - Judah, Haim
AU - Shelah, Saharon
PY - 1992/11/19
Y1 - 1992/11/19
N2 - Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 (1992) 185-199. Using a notion of rank for Hechler forcing we show: (1) assuming ωV1 = ωL1, 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 2ω 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 Hechler over V[r], thus answering a question of the first and second authors.
AB - Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 (1992) 185-199. Using a notion of rank for Hechler forcing we show: (1) assuming ωV1 = ωL1, 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 2ω 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 Hechler over V[r], thus answering a question of the first and second authors.
UR - http://www.scopus.com/inward/record.url?scp=0010762279&partnerID=8YFLogxK
U2 - 10.1016/0168-0072(92)90027-W
DO - 10.1016/0168-0072(92)90027-W
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AN - SCOPUS:0010762279
SN - 0168-0072
VL - 58
SP - 185
EP - 199
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 3
ER -