Combinatorial properties of classical forcing notions

Details Combinatorial properties of classical forcing notions Combinatorial properties of classical forcing notions

1993-09-09

arxiv.org/abs/math/9309205v1

Mathematics

Logic

Scientific paper

We discuss the effect of adding a single real (for various forcing notions adding reals) on cardinal invariants associated with the continuum (like the unbounding or the dominating number or the cardinals related to measure and category on the real line). For random and Cohen forcing, this question was investigated by Cicho'n and Pawlikowski; for Hechler forcing, by Judah, Shelah and myself. We show here: (1) adding an eventually different or a localization real adjoins a Luzin set of size continuum and a mad family of size omega_1; (2) Laver and Mathias forcing collapse the dominating number to omega_1 --- consequences: (A) CON(d=omega_1 + unif(L) = unif (M) = kappa = 2^omega) for any regular uncountable kappa; (B) Two Laver or Mathias reals added iteratively always force CH (even diamond); (C) Sigma^1_4-Mathias-absoluteness implies the Sigma^1_3- Ramsey property; (3) Miller's rational perfect set forcing preserves the axiom MA(sigma-centered).

Affiliated with

Also associated with

No associations

Rating

Combinatorial properties of classical forcing notions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Combinatorial properties of classical forcing notions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Combinatorial properties of classical forcing notions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-431638