Annals of Pure and Applied Logic 58 (3):185-199 (1992)

Abstract
Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 185–199. Using a notion of rank for Hechler forcing we show: 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; 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; 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
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DOI 10.1016/0168-0072(92)90027-w
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References found in this work BETA

Adjoining Dominating Functions.James E. Baumgartner & Peter Dordal - 1985 - Journal of Symbolic Logic 50 (1):94-101.
Jumping with Random Reals.Tomek Bartoszynski & Haim Judah - 1990 - Annals of Pure and Applied Logic 48 (3):197-213.
Why Solovay Real Produces Cohen Real.Janusz Pawlikowski - 1986 - Journal of Symbolic Logic 51 (4):957-968.

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Citations of this work BETA

Solovay-Type Characterizations for Forcing-Algebras.Jörg Brendle & Benedikt Löwe - 1999 - Journal of Symbolic Logic 64 (3):1307-1323.
Regularity Properties for Dominating Projective Sets.Jörg Brendle, Greg Hjorth & Otmar Spinas - 1995 - Annals of Pure and Applied Logic 72 (3):291-307.
Proper Forcing Extensions and Solovay Models.Joan Bagaria & Roger Bosch - 2004 - Archive for Mathematical Logic 43 (6):739-750.
Amoeba-Absoluteness and Projective Measurability.Jörg Brendle - 1993 - Journal of Symbolic Logic 58 (4):1284-1290.
Combinatorial Properties of Classical Forcing Notions.Jörg Brendle - 1995 - Annals of Pure and Applied Logic 73 (2):143-170.

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