Combinatorial properties of classical forcing notions

Annals of Pure and Applied Logic 73 (2):143-170 (1995)
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Abstract

We investigate the effect of adding a single real on cardinal invariants associated with the continuum. We show:1. adding an eventually different or a localization real adjoins a Luzin set of size continuum and a mad family of size ω1;2. Laver and Mathias forcing collapse the dominating number to ω1, and thus two Laver or Mathias reals added iteratively always force CH;3. Miller's rational perfect set forcing preserves the axiom MA

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10.1016/0168-0072(94)e0028-z

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Citations of this work

Mathias absoluteness and the Ramsey property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
Combinatorics and forcing with distributive ideals.Pierre Matet - 1997 - Annals of Pure and Applied Logic 86 (2):137-201.

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References found in this work

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Δ12-sets of reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
Every analytic set is Ramsey.Jack Silver - 1970 - Journal of Symbolic Logic 35 (1):60-64.
Selective ultrafilters and homogeneity.Andreas Blass - 1988 - Annals of Pure and Applied Logic 38 (3):215-255.

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