  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).
